Download Lesson 28, SAS Triangle Congruence

WARM UP
1. Two triangles that have the same shape and size are said to be
_________________.
2. What angle is vertical to angle 2?
3. What is the measure of the complement of a 25° angle?
4. Explain why “∆𝐴𝐵𝐶 ≅ ∆𝐷𝐸𝐹” is a false statement. Write a true congruence
statement for the triangles.
LESSON 28: SAS
TRIANGLE CONGRUENCE
Geometry
INCLUDED SIDES AND ANGLES
• Included angle: the angle formed by two adjacent sides of a polygon
• Included side: the common side of two consecutive angles of a polygon
• Side-Angle-Side (SAS) Triangle Congruence Postulate: If two sides and the
included angle of one triangle are congruent to two sides and the included
angle of another triangle, then the triangles are congruent by side-angleside congruence.
EXAMPLE
What is the included side of ∠𝐴 and ∠𝐵? What is the included angle of 𝐵𝐶 and
𝐶𝐷?
A
D
B
C
EXAMPLE
Determine whether the pair of triangles is congruent by the SAS Postulate.
EXAMPLE
Find the value of 𝑥 that makes the triangles congruent.
(6𝑥 − 27)°
(4𝑥 + 7)°
EXAMPLE
Use the SAS Postulate to prove ∆𝑊𝑋𝑌 ≅ ∆𝑊𝑍𝑌 if 𝑊𝑍 ≅ 𝑊𝑋 and ∠𝑍𝑊𝑌 ≅ ∠𝑋𝑊𝑌.
W
Z
Y
X
EXAMPLE
A land dispute over two triangular parcels of land can be ended by showing
that the parcels have the same shape and size. In the figure, two sides of
each parcel of land were measured and it was found that point C is the
midpoint of both 𝐴𝐷 and 𝐵𝐸. End the dispute by proving ∆𝐴𝐵𝐶 ≅ ∆𝐷𝐸𝐶.
A
E
C
B
D
HOMEWORK QUESTIONS
CORRECTING HOMEWORK
• Get your homework out so I can stamp it.
• If you do not have your homework complete, write your name on the board.
• Use red pen/pencil to correct.
• Trade with someone who has the homework done.
• If you didn’t get it done, you need to be working on finishing it now.
Remember no cheating and no work = no credit.
• Make sure you write CB with your name or you will lose your citizenship points
for today.
HOMEWORK
1st and 2nd hour: Lesson 28: A-D, 5, 9, 13, 14, 15, 17, 19, 20, 21, 22, 23, 24, 25, 26,
29, 30
3rd hour: Lesson 28: A-D, 9, 13, 14, 15, 17, 20, 21, 23, 24, 26, 30