6A) Using the alternate angles theorem, we know that if two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent. Therefore, angle EAB is congruent to angle BDC, and angle DCB is congruent to angle AEB. Vertical angles are the angles that are vertically opposite to each other when two lines intersect. This means angles ABE and CBD are congruent.
∠EAB = ∠BCD
∠DCB = ∠AEB
∠ABE = ∠CBD
The triangles are similar.
6B) Because there are no angles to help prove whether the two triangles are similar, we must rely on the side lengths. Lets compare the side lengths using ratios.
Left side = 12/4
Right side = 76/19
Bottom side = 76/19
12/4 : 76/19 : 76/19 = 4 : 4 : 4
The scale difference of the triangles is 4, they are similar.
7) To find the height of the building, we must first find the scale difference of the two triangles. We already know the triangles are similar. Note: m is a unit, not a variable.
Knowing the triangles are similar, all we need to find the scale is one side of each, we will use the bottom.
8m / 0.2m = 40m
The large triangle is 40 times larger than the small one.
40 times the height of the small triangle is equal to the height of the building.
40m * 1m = 40m
The building is 40 meters tall.
I hope you found my explanations helpful! Please feel free to comment on my profile if you have more questions, I will happily help. Have a great Thanksgiving!
