Congruent Triangles

Helpful websites

• http://www.regentsprep.org/Regents/mathb/1c/preprooftriangles.htm

• http://www.mathwarehouse.com/geometry/congruent_triangles/

• http://www.cliffsnotes.com/WileyCDA/CliffsReviewTopic/Congruent-Triangles.topicArticleId-18851,articleId-18788.html

4-1 Congruent Figures

Objective: To recognize congruent figures and their

corresponding parts

Vocabulary/ Key Concept

• Congruent polygons- two polygons are

congruent if their corresponding sides and angles are congruent

• If two angles in a triangle are congruent to two angles in another triangle, then the third angles are congruent.

Each pair of polygons are congruent. Find the measure of each numbered angle

• M1 = 110• m 2 = 120

• M3 = 90• m 4 = 135

WXYZ JKLM. List 4 pairs of congruent sides and angles.

• WX JK• XY KL• YZ LM• ZW MJ

• W J• K X• Y L• Z M

Determine if the polygons are congruent. Explain.

1.G I , GJH IJH,2.GHJ IHJ 3. JI GJ, GH IH,4. JH JH

GHJ and IHJ are congruent because all corresponding angle and sides are congruent

1.Given –congruent markings2.If two angles in a triangle are congruent

to two angles in another triangle, then the third angles are congruent.

3.Given-congruent markings4.Reflexive

Determine if the polygons are congruent. Explain.

1.Q T2.QSR TSV3.R VNo, the triangles do no

have corresponding sides that are congruent

1.Given – congruent measures2.Vertical angles3. If two angles in a triangle are

congruent to two angles in another triangle, then the third angles are congruent.

PROOF

Statement1. LM QP LN QN MN PN L Q2. LNM QNP 3. P M4. LMN QPN

Reasons1. GIVEN2. VEERITCAL ANGLES3. If two angles in a

triangle are congruent to two angles in another triangle, then the third angles are congruent

4. 4. Def. of congruent polygons

4-2 Congruent Triangles by SSS and SAS

Objective:To prove two triangles are congruent using SSS

and SAS Postulates

Key Concepts

• SSS – Side-side-side corresponding congruence.

• SAS – Side-Angle-Side corresponding Congruence.

ANGLE MUST BE IN BETWEEN THE TWO SIDE

Determine if you can use SSS or SAS to prove two triangles are congruent. Write the congruence statement.

ABD CBD by SAS

AB CB --CONGRUENCE MARKING BD BD -- REFLEXIVEABD CBD –CONGRUENCE MARKING

Determine if you can use SSS or SAS to prove two triangles are congruent. Write the congruence statement.

What do you know?NP = QP -- CONGRUENT MARKSNR = QR -- CONGRUENT MARKSRP = RP -- REFLEXIVE PROPERTY OF

PRN PRQ by SSS

Determine if you can use SSS or SAS to prove two triangles are congruent. Write the congruence statement.

EM PQ EN PR CONGRUENCE MARKINGN R

Not possible

Proof

Statements 1. AB DC, BAC DCA2. AC CA3. ABC CDA

Reasons1. Given2. Reflexive property of 3. SAS

A B

D C

Try: Write a proof.

Statement1. EF GF, HF DF2. DFE HFG3. DFE HFG

Reasons1. Given2. Vertical angles3. SAS

4-3 Congruent Triangles by AAS and ASA

Objective:To prove two triangles are congruent using AAS

and ASA Postulates

Key Concepts

• ASA – Two angles and an included side.

• AAS – Two angles and a non-included side.

SIDE IS IN BETWEEN THE ANGLES

Determine if you can use ASA or AAS to prove two triangles are congruent. Write the congruence statement.

TUV VST by ASA

not possible

BCEDCF by AAS

Write a Proof

Statement 1. KL ML, K M2. JLK PLM3. JKL PML

Reasons 1. Given2. Vertical angles3. ASA

What did you learn today?

• What are some simple steps to writing proofs?

• What are the four ways to prove triangles are congruent?