Congruence and Triangles

Unit 1B2 Day 2

Tell whether it is possible to create each of the

following: acute scalene triangle obtuse equilateral triangle right isosceles triangle scalene equiangular triangle right scalene triangle

Do now

Informal: Two figures are congruent if they have exactly

the same size and shapes. Two figures are congruent if and only if their

corresponding parts are congruent. Definition of congruent triangles: all _________

pairs of corresponding sides congruent; all _________ pairs of corresponding angles congruent.

Congruence

Are the two triangles congruent? Use the

definition of congruent triangles. If so, write a congruence statement.

Ex. 1: Proving Congruence

In the diagram, NPLM ≅ EFGH. Find the

values of x and y.

Ex. 1A: Congruent Figures

If two angles of one triangle are

congruent to two angles of another triangle, then ______________________

__________________________________

Third Angles Theorem

Find the value of x.

Ex. 2: Third Angles Theorem

In the diagram, ABCD ≅ KJHL. Find the values

of x and y.

Ex. 2A

Determine whether the triangles are

congruent. Justify your reasoning.

Ex. 3: Determining Congruence

Decide whether the triangles are congruent.

Justify your reasoning.

Ex. 3A

Given: AB || DC, AB ≅ DC, E is the midpoint of

BC and AD. Prove: ΔAEB ≅ ΔDEC

Ex. 4: Proving Congruence

Reflexive property of congruent

triangles: Every triangle is congruent to ____________.

Symmetric property of congruent triangles: If ΔABC ≅ ΔDEF, then _________________

Transitive property of congruent triangles: If ΔABC ≅ ΔDEF and ΔDEF ≅ ΔJKL, then ______________.

Properties of Congruent Triangles

If ΔGHJ ≅ ΔMNP, what

corresponding angles and sides are congruent?

Closure