9.2/9.3 similar triangles and proportions learning objective: to use special rules to prove...
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9.2/9.3 Similar Triangles and ProportionsLearning Objective: To use special rules to prove triangles are similar and to
write proportions to find measures in similar figures.
1. Name the triangles that appear to be similar.
Warm-up (IN)
A
B
DE
CAssume the triangles in #1 are similar.
2. Write 2 true proportions.
3. If AB=6, AE=8 and AC=7, find AD.
4. If CD=12, AD=15 and BE=10, find AE.
~ACD ABE
19
3
12.5
Notes
Learning Objective: To use special rules to prove triangles are similar and to write proportions to find measures in similar figures.
AA Similarity•2 Corresponding angles are congruent
SAS Similarity•2 Corresponding sides are in proportion•The included angle is congruent
3 ways to prove triangles are similar!
SSS Similarity•3 Corresponding sides are in proportion
EX 1 – Given: and are rt. s
Prove: ~
NHK LMK
NHK LMK
L
H
M
NK
CKC p. 456!
Learning Objective: To use special rules to prove triangles are similar and to write proportions to find measures in similar figures.
Learning Objective: To use special rules to prove triangles are similar and to write proportions to find measures in similar figures.
Triangle Proportionality Thm
If a segment is // to one side of a triangle and intersects the other 2 sides, then it divided those sides proportionally.
EC
N
A
D
If // ,AC DE then DA EC
AN CN
Learning Objective: To use special rules to prove triangles are similar and to write proportions to find measures in similar figures.
Midsegment Thm
If the midpoints of 2 sides of a triangle are joined by a segment, then
H
G
U
A
Lthe segment is // to the 3rd side and half as long
Properties of Proportions
See p. 463
EX 2 – Find each value
Learning Objective: To use special rules to prove triangles are similar and to write proportions to find measures in similar figures.
EC
N
A
D6
9
a. EC
CN=DA
AN6
=9
b. AC
DE=AN
DN
6=
15
c. EC
EC CN6
=6 9
6=
15
CKC p. 464 on paper!
HW – p. 456 #1-7,
p. 464 #1-6,14-16,21
Out – Describe 3 ways to show two triangles are similar.
Summary – Now I’m thinking…
POW!!