Unit 4: Triangle Congruence

Unit 4 Learning Targets 

LT 4-1: I can determine if 2 polygons are congruent.

LT 4-2: I can find missing angles and side lengths in Isosceles Triangles.

LT 4-3: I can determine 2 triangles congruent by SAS or SSS.

LT 4-4: I can determine 2 triangles congruent by ASA or AAS.

LT 4-5: I can determine congruence in right triangles.

LT 4-6: I can determine congruence in overlapping triangles.

LESSON 4-1

Congruence

Figures that have the same size and shape are congruent. If a rigid motion or composition of rigid motions can map one figure onto another, then the figures are congruent.

Help Videos:

●       How Do You Identify a Congruence Transformation?

●       What Makes Two Figures Congruent?

Practice:

4-1 Math XL

LESSON 4-2

Isosceles and Equilateral Triangles

An isosceles triangle has congruent base angles and legs. The angle bisector of the vertex angle of an isosceles triangle is also the perpendicular bisector of the base. An equilateral triangle is also equiangular.

Help Videos:

●       How Do You Find Missing Angles in an Isosceles Triangle Using Right Triangles?

●       Why Are the Angles of Equilateral Triangles Always Equal to 60º?

Practice:

4-2 Math XL

LESSON 4-3

Proving and Applying the SAS and SSS Congruence Criteria

If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, the triangles are congruent. If three sides of one triangle are congruent to three sides of another triangle, the triangles are congruent. If two triangles are congruent, then all corresponding angles and sides are congruent.

Help Videos:

●       What Is CPCTC?

●       What Is the Side-Side-Side Postulate for Triangle Congruence?

Practice:

4-3 Math XL

LESSON 4-4

Proving and Applying the SAS and SSS Congruence Criteria

If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, the triangles are congruent. If three sides of one triangle are congruent to three sides of another triangle, the triangles are congruent. If two triangles are congruent, then all corresponding angles and sides are congruent.

Help Videos:

●       What Is CPCTC?

●       What Is the Side-Side-Side Postulate for Triangle Congruence?

Practice:

4-4 Math XL

LESSON 4-5

Congruence in Right Triangles

Two triangles can be proven congruent without showing that all corresponding parts are congruent. Right triangles can be proven congruent using one pair of right angles, a pair of hypotenuses, and a pair of legs.

Help Videos:

●       What Is the Hypotenuse-Leg Congruence Theorem?

●       How Do You Determine If Triangles on the Coordinate Plane Are Congruent?

Practice:

4-5 Math XL

LESSON 4-6

Congruence in Overlapping Triangles

When a figure includes triangles that overlap, sides and angles can be shown congruent using the appropriate addition postulates. It is often helpful to sketch needed triangles separately in order to solve problems with overlapping triangles.

Help Videos:

●       How Do You Identify Common Parts in Overlapping Triangles?

●       How Do You Prove That Two Overlapping Triangles Are Congruent?

Practice:

4-6 Math XL

Unit 4 Vocabulary

●       congruence transformation

●       congruent figures