Similar Triangle Proofs

Page 5-7

A

CBHF

E

Similar Triangle Proof Notes

To prove two triangles are similar, you only need to prove that 2 corresponding angles are congruent.

After proving similar triangles, you can add the following two steps

- Corresponding sides of similar triangles are in proportion - The product of the means equals the product of the extremes

A

CBHF

E

EH

AC

EF

AB .2

Similar Triangle Proof Notes

Statement Reason

2. Corresponding sides of similar triangles are in proportion

ACEFEHAB .3 3. The product of the means equals the product of the extremes

EFHABC ~ .1 AAAA .1

Statement Reason

1. Given

2. Given

Pg. 6 #1

angleright a is 1. A

UTHMAH Δ~Δ .6 AAAA .6

angleright a is .3 UTH 3. Perpendicular segments

form a right angle

AHUT 2.

HH .5 5. Reflexive postulate

TH

AH

UT

MA .7 7. Corresponding sides

of similar triangles are in proportion

UTHA .4 4. All right angles are congruent

Statement Reason

1. Given

2. Parallel lines cut by a transversal form congruent alternate interior angles

Pg. 6 #2

DEAB 1.

EDCABC Δ~Δ .3 AAAA .3

DB EA

2.

EC

AC

ED

AB .4 4. Corresponding sides

of similar triangles are in proportion

Statement Reason

1. Given

2. Vertical angles are congruent

Pg. 6 #4

CDEEBC 1.

EDFCBF Δ~Δ .3 AAAA .3

21 2.

FE

FC

FD

FB .4 4. Corresponding sides

of similar triangles are in proportion

Statement Reason

1. Given

2. Given

Pg. 6 #5

EDCADC~ΔΔ .5 AAAA .5

anglesright

are 2 and 1 .3 3. Perpendicular segments form right angles

DECDAC 2.

21 .4 4. All right angles are congruent

EC

ED

AC

AD .6 6. Corresponding sides of

similar triangles are in proportion

BCAE 1.

EDACECAD .7 7. The product of the means equals the product of the extremes

Statement Reason

1. Given

2. Given

Pg. 7 #27

BCAC 1.

BCDACD Δ~Δ .5 AAAA .5

21 .4 4. An angle bisector divides an angle into two congruent parts

BA .3 3. Angles opposite congruent sides of a triangle are congruent

C bisects 2. CD

Statement Reason

1. Given

2. Given

Pg. 7 #29

TSRLMR~ΔΔ .6 AAAA .6

anglesright

are 2 and 1 .3 3. Perpendicular segments form right angles

21 .4 4. All right angles are congruent

RSTS 1.

RSLM 2.

RR .5 5. Reflexive postulate

If LM=6, TS=9 and MS=4, find RM

49

6

x

x

xx 9)4(6

xx 9246

x324 x8

Statement Reason

1. Given

2. Given

Pg. 7 #30

ADEABC~ΔΔ .6 AAAA .6

anglesright

are 2 and 1 .3 3. Perpendicular segments form right angles

21 .4 4. All right angles are congruent

ACBC 1.

ABDE 2.

AA .5 5. Reflexive postulate

If DE=5, AD=6 and AB=18, find BC

18

65

x

x690

x15

15BC