Proving Triangle Similarity with Parallel Lines

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.

Tags

CCSS.HSG.SRT.B.5

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.

Tags

CCSS.HSG.SRT.B.5

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

Tags

CCSS.HSG.CO.C.9

To find the height of a lamppost at a park, Rachel placed a mirror on the ground 20 feet from the base of the lamppost. She then stepped back 4 feet so that she could see the top of the lamp post in the center of the mirror. Rachel's eyes are 5 feet 6 inches above the ground. What is the height, in feet, of the lamppost?

• 55 feet

• 27.5 feet

• 14.5 feet

• 7.27 feet

Tags

CCSS.HSG.SRT.B.5

• Not Similar
• Similar. ∆ABC~∆EDF
• Similar. ∆ACB~∆EDF
• Similar. ∆ABC~∆EFD

Tags

CCSS.HSG.SRT.A.2

• SAS
• SSS
• AA
• not enough information to prove similarity

Tags

CCSS.HSG.SRT.B.5

Complete the two column proof by writing the number of each statement in the box the statement goes in.​

• Given

• Angle D is congruent to Angle A

• Angle B is Congruent to Angle B

• Angle Angle

Tags

CCSS.HSG.SRT.A.2

• Not Similar
• Similar. ∆MNP~∆RQS
• Similar. ∆MNP~∆QRS
• Similar. ∆NPM~∆QRS

Tags

CCSS.HSG.SRT.A.2

Is Line BC parallel to Line DE?

• Yes, because the sides are proportional creating similar triangles

• No, because the sides are not proportional therefore the triangles are not similar

Tags

CCSS.HSG.SRT.B.4

Calculator Permitted

• 
• 
• 
• 

Tags

CCSS.HSG.SRT.A.2