Download REVIEW OF SOME BASIC IDEAS

Section 8-3 Similar
Triangles
GEOMETRY
ENTRY TASK – TWO LEVELS
Medium/Difficult
F
Medium:
Given: ∠ACB ≅∠EDB and 𝐴𝐵 ≅ 𝐵𝐸
Prove: ΔABC ≅ ΔEBD
Homework Review
Short Cuts for Similar Triangles
AA
ASA
SSS
AA Similarity Postulate
If two angles of one triangle are congruent to two
angles of a second triangle, then the triangles are
similar.
This means that corresponding angles are
congruent and corresponding sides are
proportional!
SAS Similarity Theorem
If an angle of one triangle is congruent to an angle of
a second triangle, and the sides that include the two
angles are proportional, then the triangles are similar.
This means that corresponding angles are
congruent and corresponding sides are
proportional!
SSS Similarity Theorem
If the corresponding sides of two triangles are
proportional, then the triangles are similar.
This means that corresponding angles are
congruent and corresponding sides are
proportional!
Example 1
• Explain why the triangles are similar and write a similarity
statement. Then find DE.
10
16
18
12
24
Example 2
In the sunny desert a cactus casts a 9 foot shadow. At the same time
a 6 foot tall person, standing next to the cactus, casts a 4 foot
shadow. How tall is the cactus?
Example 3
Explain why the triangles are similar and write a similarity
statement. Then find the value of x.
9
6
Example 4
A photograph measuring four inches wide and five inches
long is enlarged to make a wall mural. If the mural is 120
inches wide, how long is the mural?
Example 4 – Proofs Using Triangle
Similarity
Given: PR = 2NP,
PQ = 2MP
Prove:∆𝑀𝑁𝑃 ~ ∆𝑄𝑅𝑃
Example 5 – Proofs Using Triangle
Similarity
Given: 𝐴𝐵 𝑝𝑎𝑟𝑎𝑙𝑙𝑒𝑙 𝑡𝑜 𝐶𝐷 and 𝐵𝐶 𝑝𝑎𝑟𝑎𝑙𝑙𝑒𝑙 𝑡𝑜 𝐷𝐺
Prove: 𝐴𝐵 ∙ 𝐶𝐺 = 𝐶𝐷 ∙ 𝐴𝐶
Homework
Page 455
Problems: 7-13, 19, 23, 26