In Exercises 1-3, decide whether enough information is given to prove that the triangles are congruent using either the SSS Congruence Theorem (Theorem 5.8) or the HL Congruence Theorem (Theorem 5.9). Explain.

In Exercises 1-3, Decide Whether Enough Information Is Given To Prove That The Triangles Are Congruent

Answers

Answer 1

The congruency proofs that can be used for each of the triangles are;

1) SSS Congruency

2) None

3) HL Congruence

How to prove the triangle congruency postulate?

1) The SSS congruency postulate states that If three sides of one triangle are congruent to three sides of a second triangle, then the two triangles are congruent.

Now, we see that we are shown 2 corresponding sides that are congruent. However, the third side is automatically congruent using the reflexive property of congruence.

Thus, we conclude that the congruency can be proved using SSS Congruency postulate.

2) In this one, we are given 2 congruent sides and the included angle and so it is SAS Congruency and neither SSS nor HL congruency can be used.

3) The HL congruence Postulate states that if the hypotenuse and leg of one right triangle are congruent to the hypotenuse and leg of another right triangle, then the two triangles are congruent.

In this case, we see that the hypotenuse is congruent to itself by reflexive property of congruence while the one leg is also congruent and so we can use HL Congruence Theorem

Read more about Triangle congruence postulate at; https://brainly.com/question/29268713

#SPJ1


Related Questions

In a clothing store, 65% of the customers buy a shirt, 30% of the customers buy a pair of pants, and 20% of the customers buy both a shirt and a pair of pants. I’m f a customer is chosen at random, what is the probability that he or she buys a shirt or a pair of pants?

Answers

Answer:

The Answer will be (0.75)

Find the slope of the line (2,6) and (-2,-4)

Answers

10/8
Hope this helped

Let {u1,u2,u3} be an orthonormal basis for an inner product space V. If

v=au1+bu2+cu3
is so that ∥v∥=42, v is orthogonal to u3, and ⟨v,u2⟩=−42, find the possible values for a, b, and c.

Answers

• ||v|| = 42, which is to say

||v||² = 〈v, v

…  = 〈a u₁ + b u₂ + c u₃, a u₁ + b u₂ + c u₃〉

… = a ² 〈u₁, u₁〉 + b ² 〈u₂, u₂〉 + c ² 〈u₃, u₃〉 + 2(abu₁, u₂〉 + acu₁, u₃〉 + bcu₂, u₃〉)

… = a ² ||u₁||² + b ² ||u₂||² + c ² ||u₃||²

[since each vector in the basis for V is orthogonal to any other vector in the basis, and 〈x, x〉 = ||x||² for any vector x ]

42² = a ² + b ² + c ²

[since each vector in the basis has unit length]

42 = √(a ² + b ² + c ²)

• v is orthogonal to u₃, so 〈v, u₃〉 = 0. Expanding v gives the relation

v, u₃〉 = 〈a u₁ + b u₂ + c u₃, u₃〉

… = au₁, u₃〉 + bu₂, u₃〉 + cu₃, u₃〉

… = c ||u₃||²

… = c

which gives c = 0, and so

42 = √(a ² + b ²)

• Lastly, 〈v, u₂〉 = -42, which means

v, u₂〉 = 〈a u₁ + b u₂ + c u₃, u₂〉

… = au₁, u₂〉 + bu₂, u₂〉 + cu₃, u₂〉

… = b ||u₂||²

… = b

so that b = -42. Then

42 = √(a ² + (-42)²)   →   a = 0

So we have a = 0, b = -42, and c = 0.

The required values are, [tex]a=0,b=-42 ,c=0[/tex]

Given,

[tex]v=au_1+bu_2+cu_3[/tex]

[tex]\left\| V\right\|=42[/tex]

Computation:

Since, [tex]v[/tex] is orthogonal to [tex]u_3[/tex] then we have,

[tex]\left<v,u_3 \right> =0\\\left< v,u_2\right> =-42[/tex]

Then,

[tex]\left\| V\right\|^2=\left<v,v \right>\\=\left<au_1+bu_2+cu_3,au_1+bu_2+cu_3 \right>\\=a_2\left\|u_1 \right\|^2+b_2\left\|u_2 \right\|^2+c_2\left\|u_3 \right\|^2\\=a^2+b^2+c^2\\=a^2+b^2+c^2=42^2[/tex]

As we know,

[tex]a=\left<v_1u_1 \right>\\b=\left< v_1u_2\right>= -42\\c=\left<v_1u_3 \right> =0[/tex]

[tex]a_2+b_2+c_2=42\\a=0[/tex]

Learn More:https://brainly.com/question/13152748

I need help please fast .................

Answers

Answer:

I have no idea what sohcahtoa is but:

tan 50.1° = x/5

1.196 = x/5

multiply both sides of the equation by 5:

x = 5.98

In the diagram below, assume that all points are given in rectangular coordinates. Determine the polar coordinates for each point using values of rr such that r≥0 and values of θ such that 0≤θ<2π. Visually check your answers to ensure they make sense.

(x,y)=(2,5) corresponds to (r,θ)=

(x,y)=(−3,3) corresponds to (r,θ)=

(x,y)=(−5,−3.5) corresponds to (r,θ)=

(x,y)=(0,−5.4)corresponds to (r,θ)=

Answers

Step-by-step explanation:

We have cartisean points. We are trying to find polar points.

We can find r by applying the pythagorean theorem to the x value and y values.

[tex]r {}^{2} = {x}^{2} + {y}^{2} [/tex]

And to find theta, notice how a right triangle is created if we draw the base(the x value) and the height(y value). We also just found our r( hypotenuse) so ignore that. We know the opposite side and the adjacent side originally. so we can use the tangent function.

[tex] \tan(x) = \frac{y}{x} [/tex]

Remeber since we are trying to find the angle measure, use inverse tan function

[tex] \tan {}^{ - 1} ( \frac{y}{x} ) = [/tex]

Answers For 2,5

[tex] {2}^{2} + {5}^{2} = \sqrt{29} = 5.4[/tex]

So r=sqr root of 29

[tex] \tan {}^{ - 1} ( \frac{5}{2} ) = 68[/tex]

So the answer is (sqr root of 29,68).

For -3,3

[tex] { -3 }^{2} + {3}^{2} = \sqrt{18} = 3 \sqrt{2} [/tex]

[tex] \tan {}^{ - 1} ( \frac{3}{ - 3} ) = - 45[/tex]

Use the identity

[tex] \tan(x) = \tan(x + \pi) [/tex]

So that means

[tex] \tan(x) = 135[/tex]

So our points are

(3 times sqr root of 2, 135)

For 5,-3.5

[tex] {5}^{2} + {3.5}^{2} = \sqrt{37.25} [/tex]

[tex] \tan {}^{ - 1} ( \frac{ - 3.5}{ - 5} ) = 35[/tex]

So our points are (sqr root of 37.25, 35)

For (0,-5.4)

[tex] {0}^{2} + { - 5.4}^{2} = \sqrt{} 29.16 = 5.4[/tex]

So r=5.4

[tex] \tan {}^{ - 1} (0) = undefined[/tex]

So our points are (5.4, undefined)

The table below is comparing level of education achieved to the rate of unemployment and the median weekly earnings in 2008. Based on the information provided, the unemployment rate decreases the most when moving between which two consecutive educational levels?

Answers

Answer:

"less than high school" and" high school graduate".

Answer:

The table below is comparing level of education achieved to the rate of unemployment and the median weekly earnings in 2008.  Based on the information provided, the unemployment rate decreases the most when moving between which two consecutive educational levels?

a.

“Less than high school” and “High School Graduate”  <<<<<<<CORRECT

b.

“High school graduate” and “Some college, no degree”

c.

“Associate degree” and “Bachelor’s degree”

d.

“Professional degree” and “Doctoral degree”

 

Step-by-step explanation:

Edge2021

Watch help
In APQR, PR is extended through point R to point S,
m_QRS = (4x – 15)°, m_RPQ = (x + 1), and
mZPQR = (x - 2)°. Find mZRPQ.

Answers

Answer:

m∠RPQ = 8°

Step-by-step explanation:

m∠QRS = 4x - 15

m∠RPQ = x + 1

m∠PQR = x - 2

m∠QRS is exterior angle and m∠RPQ and m∠PQr are opposite interior angles to m∠QRS

m∠QRS = m∠RPQ + m∠PQR      {Exterior angle property of triangle}

4x - 15 = x +1 + x - 2

4x - 15 = x + x + 1-2          {Combine like terms}

4x - 15 = 2x - 1        {Subtract 2x from both sides}

4x - 2x - 15 = - 1

2x - 15 = - 1                  {Add 15 to both sides}

2x = -1 + 15

2x = 14          {Divide both sides by 2}

x = 14/2

x = 7

m∠RPQ = x + 1 = 7 + 1 = 8°

Answer: x+1 =(7)+1=8

Step-by-step explanation:


Hey y’all answers in the picture ABC or D. Plz help

Answers

Answer:

D

Step-by-step explanation:

Lets use the the chart. The (5,9) if the 5 was doubled that it would equal to 10. Now you subract 1 from it making it 9.

HELP MEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE

Answers

Answer:

6/13

Step-by-step explanation:

6/13 is the right answer. Goodluck



please someone answer this

Answers

Answer:

option 2.

the others are simultaneous equations in two unknowns but 7x-2y have the same value and the value can't be two different things at once

HURRY! What is the circumference of the circle below? Use 3.14 for π.

Answers

Answer:

2.14 divided by 5 x 2 is the ansewer

Step-by-step explanation:

Joseph and Molly each have coin collections. Joseph starts with 15 coins in his collection and adds 25 coins each month. Molly starts with 25 coins in her collection and adds 25 coins each month. How many coins would Joseph have after 3 months?

Answers

Answer:

Joseph has 90 coins after 3 months

Step-by-step explanation:

Joseph: 25x + 15

Molly: 25x + 25

x = 3

Joseph: 25(3) + 15  =  90

A 33 gram sample of a substance that's
used for drug research has a k-value of
0.1124.

Find the substances half life and the round your answer to the nearest 10th

Answers

9514 1404 393

Answer:

  6.2

Step-by-step explanation:

We presume your "k-value" is the k in the exponential decay term ...

  e^(-kt) . . . where t is the number of time units

This is 1/2 when ...

  ln(1/2) = -kt

  t = ln(1/2)/(-k) = ln(2)/k

  t = 0.69315/0.1124 ≈ 6.2

The half life is about 6.2 time units.

the probability that a student takes spanish is 70%. The probability that a student takes spanish and they are a freshman is 30% what is the probability that a randomly selected student is a freshman given that he/she takes spanish

Answers

30%....................................

Answer:  At Kennedy Middle School, the probability that a student takes Technology and Spanish is 0.087. The probability that a student takes Technology is 0.68

Step-by-step explanation: u divide

Jada is standing 10 feet from the base of a tree and spot a nest sitting on a branch.the angle of elevation from the ground where she standing to the nest 55.find the height of the nest

Answers

Answer:

Hence, the height of the tree is 14.3 feet.

What is the value of the angle marked with x?

Answers

Answer:

132

Step-by-step explanation: I'm not very sure tho

what is the measure of A, in degrees, in the figure shown?

Answers

Answer:

[tex]12.7[/tex]

Step-by-step explanation:

[tex]180 - 167.3 = 12.7 \\ < angle \: on\: a \: stright \: line \: is \: 180[/tex]

Solve (z + 6)2 = 5
{−6±5‾√}

{6±5‾√}

{5‾√±−6}

{−6+5‾√,6−5‾√}

Answers

9514 1404 393

Answer:

  (a) -6±√5

Step-by-step explanation:

  (z +6)^2 = 5 . . . . . given

  z +6 = ±√5 . . . . .  take the square root

  z = -6 ±√5 . . . . . . subtract 6

I pick a ball from a bag, replace it and then pick
another. I keep doing this until I have chosen 40 balls. If I picked out 12 yellow balls, estimate the probability of not picking out a yellow ball.

Answers

Answer:

It should be 50%

Step-by-step explanation:

It should be 50% because there are 12 yellow balls, so it should be 50%.

Hope it helps you

Space shuttle Challengerexploded because of O-ring failure shortly after it was launched. O-ring damage and temperature at time of launch for the 23 space shuttle flights that preceded the Challenger. The data is reproduced below.
Flights with O-ring damage 43 57 58 63 70 70 75
Flights with no O-ring damage 66 67 67 67 68 69 70 70 72 73 75 76 76 78 79 81
Is the mean launch temperature for flights with O-ring damage significantly less than for flights with no O-ring damage? Use 5% level of significance.

Answers

Solution :

The null and the alternate hypothesis can be stated as :

Null hypothesis

[tex]$H_0:\mu_1 \geq \mu_2$[/tex]

Alternate hypothesis

[tex]$H_a:\mu_1 \leq \mu_2$[/tex]

We known;

[tex]$\overline x_1=\frac{\sum_{i=1}^n X_i}{n_1}$[/tex]

   [tex]$=\frac{43+....+75}{7}$[/tex]

   = 62.286

[tex]$\overline x_2=\frac{\sum_{i=1}^n X_i}{n_2}$[/tex]

   [tex]$=\frac{66+....+81}{16}$[/tex]

   = 72.125

[tex]$s_1^2=\frac{\sum_{i=1}^n(X_i- \overline X_1)^2}{n_1-1}$[/tex]

    [tex]$=\frac{(43-65.5)^2+....+(75-65.5)^2}{7-1}$[/tex]

   = 116.571

[tex]$s_2^2=\frac{\sum_{i=1}^n(X_i- \overline X_2)^2}{n_2-1}$[/tex]

    [tex]$=\frac{(66-72.13)^2+....+(81-72.13)^2}{16-1}$[/tex]

   = 23.45

Therefore, calculating the test statics :

[tex]$t=\frac{\overline x_1 - \overline x_2}{\sqrt{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2}}}$[/tex]

[tex]$t=\frac{62.29-72.125}{\sqrt{\frac{116.571}{7}+\frac{23.45}{16}}}$[/tex]

[tex]$t=\frac{-9.839}{4.2566}$[/tex]

 = -2.312

Now calculating the P-value for the test as follows :

P=T.DIST(t, df)

[tex]$df=\frac{\left(\frac{s_1^2}{n_1}+\frac{s^2_2}{n_2}\right)^2}{\frac{1}{n_1-1}\left(\frac{s^2_X}{n_1}\right)^2+\frac{1}{n_2-1}\left(\frac{s^2_Y}{n_2}\right)^2}$[/tex]

[tex]$df=\frac{\left(\frac{116.571}{7}+\frac{23.45}{16}\right)^2}{\frac{1}{7-1}\left(\frac{116.571}{7}\right)^2+\frac{1}{16-1}\left(\frac{23.45}{16}\right)^2}$[/tex]

    [tex]$=\frac{328.2868}{46.36395}$[/tex]

   [tex]$\approx 7$[/tex]

P=T.DIST(t, df)

 =T.DIST(-2.31, 7)

 = 0.0270

Thus, the [tex]$\text{P-value}$[/tex] of the test is P = 0.0270 is [tex]$\text{less}$[/tex] than the level of significance [tex]$\alpha= 0.05$[/tex]. Hence the researcher can reject the null hypothesis.

Conclusion: The mean launch temperature for the flights with O ring damages less than that for the flights with no O rings.

Aiden calculated that their family used 20% of their monthly income for food, and 15% of the money spent on food was spent on snacks. If they spent $45 on snacks, what is their monthly income?

Answers

Answer:

There monthly income is 300$

Janae solved the equation 3.67 = c − 2.13 , and found the value for c. Janae's solution was c =1.54 Do you agree or disagree with her solution. Explain. Show your work. plzzz help me ill give yo a brainlyiest

Answers

Answer:

Solution;

given equation : 3.67 = c - 2.13

On solving equation, we get

c = 3.67 +2.13

c = 5.8

Hence, Janae solution is incorrect. So I disagree.

Answer: No because the answer is c =5.8 or 5.80

Step-by-step explanation:

Add 2.13 to both sides. 3.67 + 2.13 = 5.80

Find x if these are similar

Answers

Answer:

C) 28

Step-by-step explanation:

RSTV = WXYZ

WX = x

[tex]\frac{RS}{VR} =\frac{WX}{ZW} \\\\\frac{7}{3} =\frac{x}{12} \\\\3x=84\\x=28[/tex]

Suppose 60% of a large group of animals is infected with a particular disease. What is the probability that at least 2 animals are infected in a sample of size 5?
0.0870
0.3174
0.913
0.6826​

Answers

Answer:

0.6826

Step-by-step explanation:

Probabilities are used to determine the chances of events.

The probability that at least 2 animals are infected is (c) 0.913

The proportion of the animal infected is given as:

[tex]p =60\%[/tex]

The probability is then calculated using the following binomial equation

[tex]P(x) = ^nC_xp^x(1-p)^{n-x}[/tex]

In this case,

[tex]n = 2[/tex]

To calculate the probability that at least 2 animals are infected, we start by calculating the probability that not up to 2 animals are infected.

So, we have:

[tex]P(x<2) =P(0) + P(1)[/tex]

This gives

[tex]P(x<2) = ^5C_0 \times (60\%)^0 \times (1-60\%)^{5-0}+ ^5C_1 \times (60\%)^1 \times (1-60\%)^{5-1}[/tex]

Simplify

[tex]P(x<2) = 1 \times (60\%)^0 \times (40\%)^{5}+ 5 \times (60\%) \times (40\%)^{4}[/tex]

[tex]P(x<2) = 0.08704[/tex]

Using the complement rule, we have:

[tex]P(x \ge 2) = 1 - P(x<2)[/tex]

So, we have:

[tex]P(x \ge 2) = 1 - 0.08704[/tex]

[tex]P(x \ge 2) = 0.91296[/tex]

Approximate

[tex]P(x \ge 2) = 0.913[/tex]

Hence, the probability is (c) 0.913

Read more about probabilities at:

https://brainly.com/question/251701

Determine which point is part of the solution set to the following
system of inequalities: f(x) < x + 4; f(x) > - X-3; and f(x) < 5.
(0,0)
(-60)
(-3, 4)
(4,6)

Answers

I think 4,6
I had a test similar I’m not the best at it though hope this helps tho

Solve for x.
Enter the solutions from least to greatest.
(2x + 4)(3x − 2) = 0
lesser x =
greater x =

Answers

Answer:

lesser x = -2, greater x = 2/3

Step-by-step explanation:

(2x+4)= 0 ---> bring 4 to the other side

2x=-4 ----> divide by 2 on both sides

x= -4/2 = -2 ----> simplify

(3x-2)= 0 ----> bring the 2 to the other side

3x=2 ----> divide by three on both sides

x=2/3

hope this helps!

Are all rectangles and squares are parallelograms ?​

Answers

Answer:

A parallelogram has opposite sides parallel and equal in length. Also opposite angles are equal (angles "A" are the same, and angles "B" are the same). NOTE: Squares, Rectangles and Rhombuses are all Parallelograms!

Yes, they are.

Answer:

Yes

Step-by-step explanation:

Squares are quadrilaterals with 4 congruent sides and 4 right angles, and they also have two sets of parallel sides. Parallelograms are quadrilaterals with two sets of parallel sides. Since squares must be quadrilaterals with two sets of parallel sides, then all squares are parallelograms.

Hope it is helpful....

In the triangle below,
x = [ ? ] cm. Round to the
nearest tenth.
15 cm
х
350
9.00
y

Answers

Answer:

x=8.6

Step-by-step explanation:

x=8.6

Solve this expression: (2-i)(-3+i)

Answers

Answer:

-5+5i

Step-by-step explanation:

Answer:

D on edge

Step-by-step explanation:

-5+5i

Need help with this question.

Answers

9514 1404 393

Answer:

  643.72 m²

Step-by-step explanation:

The area is the sum of the areas of the parts. The figure can be divided into a triangle and a semicircle.

The formula for the area of the triangle is ...

  A = 1/2bh

For the given base of 28 m and height of 24 m, the area is ...

  A = 1/2(28 m)(24 m) = 336 m²

__

The area of a semicircle is given by the formula ...

  A = (π/8)d² . . . . for diameter d

The given diameter is 28 m, so the area is about ...

  A = (3.14/8)(28 m)² = 307.72 m²

__

Then the total area of the figure is ...

   total area = triangle area + semicircle area

   total area = 336 m² +307.72 m² = 643.72 m²

Other Questions
your system has a driver that is locked to manufacturer specifications. please try downloading the latest driver from the manufacturer's website to update. installer exit code: 1 What is SSS SAS AAS RHS? What is Carbon?Why do we care about carbon so much in science? Courtney would like to estimate the net worth of all people in the US. The distribution of net worth of people in theUS is strongly skewed to the right. Courtney selects an SRS of size n = 15 from this population and calculates thesample mean. What is the shape of the distribution of the sample mean for all possible simple random samples ofsize 15 from this population? Which account has the lowest minimum balance requirement? 10x56=4 Solution: x = A pilot was scheduled to depart at 4:00 p.m., but due to air traffic, her departure has been delayed by 16 minutes. air traffic control approved a new flight plan that will allow her to arrive four times faster than she calculated in her original flight plan. let x represent the time, in minutes, of her original flight. create an equation that can be used to predict the number of minutes after 4:00 p.m. she will arrive at her destination.a. y equals one fourth times x minus 16 b. y = 4x 16 c. y equals one fourth times x plus 16 d. y = 4x 16 wrate 10 as a fraction of 30 imprison someone for a decade for stealing 10 dollars. What ethic decision making principal does this constitutional clause MOST LIKELY reflect?answers:a:rightsb:virtuec: common goodd:fairness and justice A car owner decides to leave his car outside on a cold winter day. the next morning, the driver noticed ice on the windshield, a product of deposition. choose the best reason explaining this phenomenon. what happened? URGENT!! ILL GIVEBRAINLIEST!!!! AND 100POINTS!!! What is the effect of a quota? How did the Sherman Antitrust Act affect monopolies? Is f/x )= 3x a function? _____ is/are another way of describing a vertical hierarchy.a. A chain of commandb. An upward graphc. A network structured. Corporate stepse. An X-Y chart gina, a neutral third party, tries to resolve a conflict initiated by a manager and union representative at all sports shoes. she does so by listening to what both parties have to say about the issue and facilitating the negotiations. in this scenario, gina is exercising which type of alternative to work stoppages? Please help AFSP!!!15 points I need this by tmrw please What is the other name of Natal? there is a fundamental ambiguity at the heart of psychological egoism. this ambiguity involves the question of whether group of answer choices we are our brothers' keepers we act selfishly or in our own self-interest we have a right to government support when we fall on hard times all of the above What is the purpose of the author's argument?