Transcript Sect8-3-5 - epawelka-math

Sections 8-3/8-5:
April 24, 2012
Warm-up: (10 mins)
Practice Book:
Practice 8-2 # 1 – 23 (odd)
Warm-up: (10 mins)
Warm-up: (10 mins)
Questions on Homework?
Review
Name the postulate you can use to prove the
triangles are congruent in the following figures:
Sections 8-3/8-5:
Ratio/Proportions/Similar Figures
Objective: Today you will learn to prove
triangles similar and to use the SideSplitter and Triangle-Angle-Bisector
Theorems.
Angle-Angle Similarity (AA∼)
Postulate
 Geogebra file: AASim.ggb
Angle-Angle Similarity (AA∼)
Postulate
Example 1: Using the AA∼ Postulate, show why
these triangles are similar
 ∠BEA ≅∠DEC
because vertical
angles are
congruent
 ∠B ≅∠D because
their measures
are both 600
 ΔBAE ∼ ΔDCE by
AA∼ Postulate.
SAS∼ Theorem
ΔABC
∼
ΔDEF
SAS∼ Theorem Proof
SSS∼ Theorem
SSS∼ Theorem Proof
Example 2: Explain why the triangles are similar
and write a similarity statement.
Example 3: Find DE
Real World Example
How high must a tennis ball must be hit to just pass
over the net and land 6m on the other side?
Use Similar Triangles to find Lengths
Use Similar Triangles to Heights
Section 8-5: Proportions in Triangles
Open Geogebra file SideSplitter.ggb
Side-Splitter Theorem
Example 4: Use the Side-Splitter
Theorem to find the value of x
Example 5:
Find the value of the missing variables
Corollary to the Side-Splitter Theorem
Example 6: Find the value of x and y
Example 7: Find the value of x and y
Sail Making using the Side-Splitter Theorem
and its Corollary
What is the value of
x and y?
Triangle-Angle-Bisector Theorem
Triangle-Angle-Bisector Theorem
Proof
Example 8: Using the Triangle-AngleBisector Theorem, find the value of x
Example 9: Fnd the value of x
Theorems
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Angle-Angle Similarity (AA∼) Postulate: If two angles of
one triangle are congruent to two angles of another triangle,
then the triangles are similar.
Side-Angle-Side Similarity (SAS∼) Theorem: If an angle
of one triangle is congruent to an angle of a second triangle,
and the sides including the two angles are proportional, then
the triangles are similar.
Side-Side-Side Similarity (SSS∼) Theorem: If the
corresponding sides of two triangles are proportional, then the
triangles are similar.
Side-Splitter Theorem: If a line is parallel to one side of a
triangle and intersects the other two sides, then it divides
those sides proportionally.
Corollary to the Side-Splitter Theorem: If three parallel
lines intersect two transversals, then the segments intercepted
on the transversals are proportional.
Triangle-Angle-Bisector Theorem: If a ray bisects an angle
of a triangle, then it divides the opposite side into two
segments that are proportional to the other two sides of the
triangle.
Wrap-up
 Today you learned to prove triangles similar and to use the
Side-Splitter and Triangle-Angle-Bisector Theorems.
 Tomorrow you’ll learn about Similarity in Right Triangles
Homework (H)
 p. 436 # 4-19, 21, 24-28
 p. 448 # 1-3, 9-15 (odd), 25, 27, 32, 33
Homework (R)
 p. 436 # 4-19, 24-28
 p. 448 # 1-3, 9-15 (odd), 32, 33