Post on 22-Dec-2015
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