Download Proving Triangles Congruent (part 2)

November 01, 2016
Unit 4, Lesson 3
Proving Triangles
Congruent (part 2)
I must study politics and war that my children may have liberty to study
mathematics and philosophy. My children ought to study mathematics and
philosophy...in order to give their children a right to study painting, poetry,
music, architecture, statuary, tapestry, and porcelain.
-John Adams
Postulate 12
Side-Side-Side (SSS≅) Postulate
If three sides of one triangle are congruent to
three sides of another triangle, then the
triangles are congruent.
November 01, 2016
Postulate 13
Side-Angle-Side (SAS ≅) Postulate
If two sides and their included angle of one triangle
are congruent to two sides their included angle of
another triangle, then the triangles are congruent.
Postulate 14
Angle-Side-Angle (ASA ≅) Postulate
If two angles and their included side of one
triangle are congruent to two angles and their
included side of another triangle, then the triangles
are congruent.
122°
November 156
01, 2016
Why Side-Side-Angle doesn't work
1. Place center at B and intersect the ray
at two points, C and D
2. Draw in BC and BD
3. Trace the triangles ABC
and ABD below
Are the triangles congruent?
Why Angle - Angle - Angle does not work:
Given: Two equiangular triangles.
Do they have to be congruent?
November 01, 2016
Example 1: Can the triangles be proved congruent? Why?
If so write the congruence statement.
a)
c)
b)
d)
November 01, 2016
e)
What is the fewest requirements to show
congruent quadrilaterals?
(Start thinking about this. You're first
project is going to focus on this idea)
November 01, 2016