On the graph, two right triangles have the line as the hypotenuse. In this task, you will use these triangles to show that the slope between points E and A is the same as the slope between points A and C.


Q1:
Which angles of the triangles measure 90°?

Q2: To show that the other two angle measurements in each triangle are equal, you can use parallel lines cut by a transversal. Which two pairs of line segments formed by triangle sides are parallel, and what is the transversal for each pair?

Answer:

1.The 6th one

2. The pairs can be (6, 8)

Step-by-step explanation:

We know that, the Slope is always given as [tex]\bold{\dfrac{Rise}{Run}}[/tex], where the rise is the vertical height of the slope and run is the horizontal length of the slope.

For Δ ADE,

rise = DE = 4 units,

run = DA = 6 units,

[tex]\bold{slope = \dfrac{Rise}{Run} =\dfrac{4}{6} = \dfrac{2}{3}}[/tex]

For Δ ABC,

rise = AB = 2 units,

run = BC = 3 units,

[tex]\bold{slope = \dfrac{Rise}{Run} = \dfrac{2}{3}}[/tex],

Thus, the slope of line EA and AC is equal.

We know in a Right Angle Triangle the side opposite to the right angle is the longest side and it is known as hypotenuse.

As already mentioned in the question " two right triangles have the line as the hypotenuse", which means line EA and line AC are already said as the hypotenuse of the triangles. therefore, the angle opposite to them is the right angle in the triangles.

1.)  

In ΔABC, the hypotenuse is the line AC, therefore, the right angle is the opposite angle which is ∠ABC.

Similarly,  In ΔEDA, the hypotenuse is the line EA, therefore, the right angle is the opposite angle which is ∠EDA.

2.)

Parallel lines are those lines that always maintain the same distance between them and will never meet. whereas, a transversal is a line that crosses two or more parallel lines. As shown in the image below,

Here, there are two pairs of parallel lines cut by a transversal

Pair I:   line ED and line AB are a pair of parallel lines, can be easily seen if both the lines are extended, while AD (or x-axis), line BC(only if extended), and line EC are the transverses between them.

Pair II:  line DA and line BC are a pair of parallel lines, can be easily seen if both the lines are extended, while AB (or y-axis), line ED(only if extended), and line EC are the transverses between them.

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