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Hw-pg. 245-246 (1-6, 8-12)
4.4-4.5 Quiz THU 11-20, p. 5 &
FRI 11-21, p. 3 & p. 7
www.westex.org HS, Teacher Websites
11-13-14
Warm up—Geometry CPA
1. Which biconditional statement is false?
(A) x = 1 if and only if x2 = 1.
(B) Three points are collinear if and only if one
point is between the other two.
(C) An angle is a straight angle if and only if its
sides are opposite rays.
(D) A polygon is a triangle if and only if it has
exactly three sides.
GOAL:
I will be able to:
1. apply SSS and SAS to construct triangles and
solve problems.
2. prove triangles congruent by using SSS and
SAS.
HW-pg. 245-246 (1-6, 8-12)
4.4-4.5 Quiz THU 11-20, p. 5 & FRI 11-21, p. 3 & p. 7
www.westex.org
HS, Teacher Websites
Name _________________________
Date ________
Geometry CPA
4.4 Triangle Congruence SSS & SAS
GOAL:
I will be able to:
1. apply SSS and SAS to construct triangles and solve problems.
2. prove triangles congruent by using SSS and SAS.
In Lesson 4-3, you learned that triangles that are congruent have all six pairs of
corresponding parts congruent. The property of triangle rigidity states that if the side
lengths of a triangle are given, the triangle can have only one shape. As a result you only need
to know that two triangles have three pairs of ________ _______________ __________.
Example 1: Using SSS to Prove Triangle Congruence
Use SSS to explain why ∆ABC  ∆DBC.
YOU TRY:
Use SSS to explain why ∆ABC  ∆CDA.
An __________________ is an angle formed by two adjacent sides of a polygon.
B is the included angle between sides AB and BC.
It can also be shown that only two pairs of
 corresponding sides are needed to prove the
congruence of two triangles if the included angles are also .
Caution
The letters SAS are written in that order because the congruent angles
must be between pairs of congruent corresponding sides.
Example 2: Engineering Application
The diagram shows part of the support structure for a tower.
Use SAS to explain why ∆XYZ  ∆VWZ.
YOU TRY:
Use SAS to explain why ∆ABC  ∆DBC.
Example 3: Verifying Triangle Congruence
Show that the triangles are congruent for the given value of the variable.
∆MNO  ∆PQR, when x = 5.
YOU TRY:
What value of y would show that ∆STU  ∆VWX? Are they congruent by SAS or SSS?
Example 4: Proving Triangles Congruent
Given: BC ║ AD, BC  AD
Prove: ∆ABD  ∆CDB
Statements
Reasons
YOU TRY:
Prove: ∆RQP  ∆SQP
Statements
Reasons
4.4 Practice
1. Show that ∆ABC  ∆DBC, when x = 6.
Which postulate, if any, can be used to prove the triangles congruent?
2.
3.