Transcript Prove that the triangles are similar.

7-3: Proving Triangles are
Similar
Rigor: 1) Prove 2 triangles are similar
2) Use similar triangles to solve indirect measurement problems
Relevance : Logic and proof, indirect measurement
Similarity Recap: Finish the sentence
Two figures are similar if there is one or more
________________ that will map one figure onto the other.
The 4 similarity transformations are ________
The corresponding angles of similar figures are ______
The corresponding side lengths of similar figures are ____
The corresponding sides of dilated figures are __________
3 Triangle Similarity Criterion
(AA ~) – If 2 pairs of corresponding
angles are congruent, the ∆s are ~.
(SSS ~) – If all corresponding sides are
proportional, the ∆s are ~.
(SAS ~) – If 2 pairs of corresponding sides
are proportional and the included angle
pair is congruent, the ∆s are ~.
Dissecting Similarity Statements
Turn to core book page 298
Complete example 2 and the reflection
problems on your own.
Be ready to discuss reflection questions in
a few minutes
EX 1: Are the triangles similar? Justify your answer.
EX 2: Prove that the triangles are similar.
A)
B)
EX 3:
Indirect Measurement: One of my favorite
applications of Geometry!
One method of indirect measurement
is using similarity proportions of triangles!
Used to calculate the height of
pyramids & mountains, width of rivers, etc.
Ancient Greek philosopher Eratosthenes
even used similar triangles to approximate
the circumference of the earth!
EX 4: What is the height of the cliff?
EX 5: Using Indirect Measurement
A birdbath 2ft 6in tall casts an 18in shadow in a
garden at the same time an oak tree casts a 90ft
shadow. How tall is the tree?
7-3 Classwork from the textbook
Heading: 7-3 CW pg 486
Problems: #2 – 10 evens, 16 – 18, 23, 24
7-3 Homework from the core book
Page 301 and 302 ALL
Due Thurs/Fri