Holt McDougal Geometry

4-3 Congruent Triangles

Warm Up1. Name all sides and angles of ∆FGH.

2. What is true about K and L? Why?

3. What does it mean for two segments to be congruent?

FG, GH, FH, F, G, H

;Third s Thm.

They have the same length.

Holt McDougal Geometry

4-3 Congruent Triangles

Use properties of congruent triangles. Goals of the Day!

Holt McDougal Geometry

4-3 Congruent Triangles

Terms (Add to your definition sheet)• Congruent figures – Two figures

whose corresponding sides and corresponding angles are congruent.

Holt McDougal Geometry

4-3 Congruent Triangles

Holt McDougal Geometry

4-3 Congruent TrianglesDescribing Congruent Triangles

• In the diagram ΔMLK ≅ ΔJTEComplete the statements.1.∠L ________≅

2.MK ________≅

3.m M = ______∠ °4.m T =_______∠ ° 5.ML ________≅

6.ΔETJ _______ ≅

Holt McDougal Geometry

4-3 Congruent Triangles

Holt McDougal Geometry

4-3 Congruent Triangles

Two vertices that are the endpoints of a side are called consecutive vertices.For example, P and Q are consecutive vertices.

Helpful Hint

Holt McDougal Geometry

4-3 Congruent Triangles

To name a polygon, write the vertices in consecutive order. For example, you can name polygon PQRS as QRSP or SRQP, but not as PRQS.

How to name a polygon!

Holt McDougal Geometry

4-3 Congruent Triangles

When you write a statement such as ABC DEF, you are also stating which parts are congruent.

Helpful Hint

Holt McDougal Geometry

4-3 Congruent TrianglesExample 1: Naming Congruent Corresponding Parts

Given: ∆PQR ∆STWIdentify all pairs of corresponding congruent parts.Angles: P S, Q T, R W

Sides: PQ ST, QR TW, PR SW

Holt McDougal Geometry

4-3 Congruent Triangles

Warm Up• In the diagram ΔMLK ≅ ΔJTEComplete the statements.1.∠E ________≅

2.LK ________≅

3.m E = ______∠ °4.m T =_______∠ ° 5.LM ________≅

6.ΔKML _______ ≅

Naming Congruent Figures• Write the angle congruence statements

– ∠A C Given≅ ∠– ∠D B Given≅ ∠– ∠B D Given≅ ∠

• Write the side congruence statements – AD CB Given≅– AB CD Given≅– BD BD Reflexive≅

• Therefore ΔADB ≅ ΔCBD A C

D B B D

Naming Congruent Figures• Identify any figures that can be proved

congruent. Explain your reasoning. For those that can be proved congruent, write a congruent statement.

When two figures are not congruent.

∠M ≅ ∠O Given∠N ≅ ∠P Given

∠Q ≅ ∠Q Reflexive

Sides ??? Not Enough Information, so triangles are not congruent.

Holt McDougal Geometry

4-3 Congruent Triangles

Given: ∆ABC ∆DEF

Example: Using Algebra and Congruent Triangles

Find the value of x.

2x – 2 = 62x = 8x = 4

Add 2 to both sides.

Divide both sides by 2.

Substitute values for AB and DE.

AB = DE

First: Redraw the triangles so they are oriented in the same positions.

Mark off the congruent sides with hash marks!

Holt McDougal Geometry

4-3 Congruent Triangles

Given: ∆ABC ∆DEF

Find the measure of the missing angle

Find mF.

mEFD + mDEF + mFDE = 180°

mEFD + 53 + 90 = 180

mF + 143 = 180

mF = 37°

∆ Sum Thm.

Substitute values for mDEF and mFDE.

Simplify.

Subtract 143 from both sides.

Holt McDougal Geometry

4-3 Congruent Triangles

Using Algebra

Holt McDougal Geometry

4-3 Congruent Triangles

Try this one

Holt McDougal Geometry

4-3 Congruent TrianglesLesson Quiz

1. ∆ABC ∆JKL and AB = 2x + 12. JK = 4x – 50. Find x and AB.

Given that polygon MNOP polygon QRST, identify the congruent corresponding part.2. NO ____ 3. T ____

31, 74

RS P

Holt McDougal Geometry

4-3 Congruent Triangles

Assignment

• P 234 3-10, 13-18, 23-25