Congruence and Triangles

Congruent Figures

• Two plane figures are congruent if they are the same size and shape - that is, if their corresponding angles are equal and their corresponding sides are equal.

http://www.math.com/school/subject3/lessons/S3U3L1GL.html

∠A P≅ ∠

∠B Q≅ ∠

∠C R≅ ∠

Corresponding Angles

Corresponding Sides

PQAB ≅QRBC ≅

PRAC ≅

Example 1

Corresponding Angles

Corresponding Sides

a. Find the value of x.

b. Find the value of y.

∠D K≅ ∠∠E L≅ ∠

∠F M≅ ∠

∠G N≅ ∠

KLDE ≅LMEF ≅MNFG ≅

KNDG ≅

Theorem 4.3 – Third Angles Theorem

• If two angles of one triangle are congruent to two angles of another triangle, then the third angles are congruent.

Example 2- Using the 3rd Angle Theorem

• Find the value of x in the diagram.

Example 3 – Determining whether triangles are congruent

• Decide if the triangles are congruent. Justify your reasoning.

Homework

• Exercise 4.2 page 205: 1-39, odd.