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CONGRUENT
TRIANGLES
Chapter 4 – Geometry B – Fall 2013
4.1 Triangles and Angles
Classify triangles by their sides and angles.
Find angle measures in triangles.
Triangles

Triangles are figures with three sides.

We can classify triangles by their sides and angles.
Classifying Triangles by Sides
Classifying Triangles by Angles
Example 1

Classify each triangle by its sides and angles.
Angles in a Triangle

The angles inside a triangle add up to 180°.

Example 2: Find the value of x.
Angles in a Triangle


The measure of an exterior angle to a triangle is
equal to the sum of the two angles that are not
adjacent to it.
Example 3: Find the value of x.
Classwork

Complete Worksheet 4.1 Practice B
Homework 10/15

Complete Worksheet 4.1 Practice A

Skip #1-5
4.2 Congruence & Triangles
Identify congruent figures and corresponding
parts.
Write congruence statements.
4.1 Check
Congruent Triangles


Recall: Congruent means _________________
Congruent Triangles have 3 equal sides and 3 equal
angles.
When we write the congruence
statement _______________ the
order of the points matters! The
order of the vertices should match
(use the angles as a guide).
Corresponding Sides & Angles



Corresponding means “matching”.
Corresponding Sides are the sides in two
congruent triangles that are equal.
Corresponding Angles are the angles in two
congruent triangles that are equal.
Identifying Corresponding Parts

Identify the corresponding sides and angles in the
two congruent triangles below.
Example 1


Are the two triangles congruent? How do you know?
Write a congruence statement and identify all
corresponding sides and angles.
Example 2


Is <C = <K? How do you know?
Find the value of x.
Homework 10/16

Complete Worksheet 4.2 Practice A
Warm Up 10/17

Complete the problems on the worksheet
independently!
Classwork 10/17

Ch. 4.1: p. 198 #16-21, 31-39

Ch. 4.2: p. 206 #10-17, 22, 25

Homework: Study for Quiz! p. 210 #1-6
4.3 SSS & SAS
Prove that triangles are congruent using SSS and
SAS.
Included Angle

An included angle is the angle between two sides.
Name the included angle between the pair of sides given:
a. DF and FE
b. DE and EF
c. DF and ED
Proving Triangles are Congruent



We don’t always need to know that all the angles and
all the sides are the same to say that two triangles are
congruent.
There are several shortcuts that we can use that only
require us to know that 3 things are congruent.
They work because knowing just some information
can allow us to determine that all sides and angles are
equal.
SSS: Side-Side-Side

If all three sides are congruent, then the triangles
must be congruent.
SAS: Side-Angle-Side

If two sides and their INCLUDED ANGLE are
congruent, then the triangles must be congruent.
Examples

Determine whether there is enough information to
prove that the triangles are congruent. If yes, state
the reason why you know they are congruent.
Classwork 10/18

4.3 p. 216 #12-19
Homework 10/18

4.3 Worksheet Practice A
4.4 ASA & AAS
Prove that triangles are congruent using ASA and
AAS.
ASA: Angle-Side-Angle

If two angles and their INCLUDED SIDE are
congruent, then the triangles must be congruent.
AAS: Angle-Angle-Side

If two angles and their NON-INCLUDED SIDE
are congruent, then the triangles must be congruent.
We CANNOT Use:

AAA

ASS
Examples

Determine whether there is enough information to
prove that the triangles are congruent. If yes, state
the reason why you know they are congruent.
Examples

Determine whether there is enough information to
prove that the triangles are congruent. If yes, state
the reason why you know they are congruent.
Classwork 10/21

4.4 p. 223 #2-13
Homework 10/21

Triangle Congruence “Study Guide” – both sides!
4.5 Using Congruent Triangles
Determine missing information needed to prove
two triangles congruent.
Digging Deeper…


What information is missing that would tell me that
two triangles are congruent?
If I know that two triangles are congruent, what
other sides and angles (not marked) do I now know
are congruent?
What information is missing that would
tell me that two triangles are congruent?

What information would I need to know to prove
…
By SAS?
B

By ASA?
F
E
A
D

By AAS?
C
If I know that two triangles are congruent, what other sides
and angles (not marked) do I now know are congruent?

State the reason why the two triangles are congruent.
Name all additional corresponding sides and angles.
F
B
A
C
J
E
D
G
H
Classwork

Complete Worksheet 4.5 Practice A
Homework

Complete Congruent Triangles Worksheet
4.6 Properties of Special Triangles
Use properties of isosceles, equilateral, and right
triangles to find missing side and angle measures
in triangles.
Equilateral = Equiangular

All equilateral triangles are equiangular.

Or simply: All angles equal = All sides equal
B
A
C
Isosceles Triangles
Sides


Legs: The two equal sides
Base: The third side
Angles


Base Angles: The two equal angles (on the base)
Vertex Angle: Angle across from the base.
Isosceles Triangle


If we know two sides are equal, then the two base
angles are equal (and vice versa!)
Example 1: Solve for x and y.
Isosceles Triangles

Example 2: Solve for y.
Right Triangles


Legs: The two sides that make up the right angle.
Hypotenuse: The side across from the right angle.
Proving Right Triangles Congruent


To prove that two right triangles are congruent, we
only need to know that the hypotenuse and one of
the legs are congruent.
HL = Hypotenuse – Leg
Examples

Determine whether the following right triangles are
congruent and state how you know.
Classwork

Complete Worksheet 4.6 Practice A
Homework

Complete Worksheet 4.6 Practice B