Question

Use the diagram and flow chart to answer the question.

https://learning.k12.com/content/enforced/520566-COF_ID162845/12.1.4a.JPG?_&d2lSessionVal=VBwU0XNnXKC2LkxrlSJuTBFyR

Ethan is proving the theorem that states that if two triangles are similar, then the measures of the corresponding angle bisectors are proportional to the measures of the corresponding sides.

Given: ∆ABC ~ ∆EFG; BD bisects ∠ABC, and FH bisects ∠EFG.

Prove: AB/EF = BD/FH

Ethan’s incomplete flow chart proof is shown.

https://learning.k12.com/content/enforced/520566-COF_ID162845/12.1.4b.JPG?_&d2lSessionVal=VBwU0XNnXKC2LkxrlSJuTBFyR

Which statement and reason should Ethan add at the question mark to best continue the proof?

A. ∆ABD ~ ∆EFH ; AA similarity

B. ∠BCA ≅ ∠FGE ; definition of similar triangles

C. AB/BC = EF/GH; definition of similar triangles

D. m∠ADB + m∠ABD + m∠BAD = 180°; m∠EFH + m∠EHF + m∠FEH = 180°; Angle Sum Theorem

Answer 1

THE FIRST PIC

Answer 2

THE SECOND PIC

Answer 3

@mhchen

Answer 4

Since the 2 steps going into the question mark are:

angle BAC is congruent to FEG
and
angle ABD is congruent to EFH


When there's 2 congruent angles for both triangles

You can prove that they are similar using the Angle-Angle Postulate

Answer 5

D CORRECT ?

Answer 6

Actually A

Since A is the Angle-Angle Postulate

Answer 7

right i thought of A at first

Answer 8

The hypotenuse of a right triangle has length 13 units, and one leg has length 12 units. How long is the other leg?

A. 17.7 units


B. -17.7 units


C. 5 units


D. -5 units

Answer 9

I BELIEVE IT IS C

Answer 10

Yes

Answer 11

Complete the proof that ∆RSU~∆RTS.

https://learning.k12.com/content/enforced/520566-COF_ID162845/12.1.5.JPG?_&d2lSessionVal=TDhDvQZm55komjdG2HDU6TVJg

https://learning.k12.com/content/enforced/520566-COF_ID162845/12.1.5.JPG?_&d2lSessionVal=TDhDvQZm55komjdG2HDU6TVJg

A. SAS similarity


B. angles forming a linear pair sum to 180 degrees


C. all right angles are congruent


D. Additive property of length


E. vertical angle theorem


F. AA Similarity


G. definition of supplementary angles


H. definition of similarity


F. Acute angles in a right triangle sum to 90 degrees