Similarity ( Review) Ms. Sanchez 2020

When two triangles are considered similar but not congruent?

• The distance between corresponding vertices are equal.

• The distance between corresponding vertices are proportionate.

• The vertices are reflected across the x-axis.

• Each of the vertices are shifted up by the same amount.

Each of the vertices are shifted up by the same amount.

• The side lengths and angle measure were multiplied by $\frac{XY}{AB}$

• The side lengths were multiplied by $\frac{XY}{AB}$ , while the angle measures were preserved.

• The angle measures were multiplied by $\frac{XY}{AB}$ , while the side lengths were preserved.

• The angle measures and side lengths were preserved.

 $In\ the\ diagram\ below,\ ∆𝐴𝐵𝐶~∆𝐷𝐸𝐹.$  
 $If𝐴𝐵=6and𝐴𝐶=8,$  

which statement will  justify  similarity  by  SAS ?

•  $𝐷𝐸=9,\ 𝐷𝐹=12,\ and∠𝐴≅∠D$  

•  $𝐷𝐸=8,\ 𝐷𝐹=10,\ and∠𝐴≅∠D$  

•  $𝐷𝐸=36,\ 𝐷𝐹=64,\ and∠𝐶≅∠𝐿F$  

•  $𝐷𝐸=15,\ 𝐷𝐹=20,\ and∠𝐶≅∠𝐿F$  

Kamal dilates triangle ABC to get triangle A′B′C′. He knows that the triangles are similar because of the definition of similarity transformations. He wants to demonstrate the angle-angle similarity postulate by proving

∠BAC≅∠B′A′C′ and∠ABC≅∠A′B′C′.

• Two non-vertical lines have the same slope if and only if they are parallel.

• Angles supplementary to the same angle or to congruent angles are congruent.

• If two parallel lines are cut by a transversal, then each pair of corresponding angles is congruent.

• If two parallel lines are cut by a transversal, then each pair of alternate interior angles is congruent.

Lines AC and FG are parallel. Which statement should be used to prove that triangles ABC and DBE are similar?

• Angles BDE and BCA are congruent as alternate interior angles.

• Angles BAC and BEF are congruent as corresponding angles.

• Angles BED and BCA are congruent as corresponding angles.

• Angles BDG and BEF are congruent as alternate exterior angles.

Given the diagram below, what is the value of x?

• 13.5

• 14.6

• 15.5

• 16.6

A scale model of the Millennium Dome in Greenwich, England, was constructed on a scale of 100 meters to 1 foot. The cable supports are 50 meters high and form a triangle with the cables. How high are the cable supports on the scale model that was built?

• 0.5 foot

• 1 foot

• 1.5 feet

• 2 feet

Hector knows two angles in triangle A are congruent to two angles in triangle B. What else does Hector need to know to prove that triangles A and B are similar?

• Hector does not need to know anything else about triangles A and B.

• Hector needs to know the length of any corresponding side in both triangles.

• Hector needs to know all three angles in triangle A are congruent to the corresponding angles in triangle B.

• Hector needs to know the length of the side between the corresponding angles on each triangle.

In ∆𝑆𝐶𝑈 shown below, points 𝑇 and 0 are on 𝑆𝑈̅̅̅̅ and 𝐶𝑈̅̅̅̅, respectively. Segment 𝑂𝑇̅̅̅̅ is drawn so that ∠𝐶 ≅ ∠𝑂𝑇𝑈.

• 5.6

• 8.75

• 11

• 15

. In the diagram below, 𝐶𝐷̅̅̅̅ is the altitude drawn to the hypotenuse 𝐴𝐵̅̅̅̅ of right triangle 𝐴𝐵𝐶.

• 𝐴𝐷 = 2 and 𝐷𝐵 = 36

• 𝐴𝐷 = 3 and 𝐴𝐵 = 24

• 𝐴𝐷 = 6 and 𝐷𝐵 = 12

• 𝐴𝐷 = 8 and 𝐴𝐵 = 17