obj. 17 congruent triangles

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Obj. 17 Congruent Triangles The student is able to (I can): Identify congruent parts based on a congruence relationship statement Identify and prove congruent triangles given Three pairs of congruent sides (Side-Side-Side) Two pairs of congruent sides and a pair of congruent included angles (Side-Angle-Side)

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Obj. 17 Congruent Triangles

The student is able to (I can):

• Identify congruent parts based on a congruence relationship statement

• Identify and prove congruent triangles given

— Three pairs of congruent sides (Side-Side-Side)

— Two pairs of congruent sides and a pair of congruent included angles (Side-Angle-Side)

congruent polygons

Geometric figures are congruent if they are the same sizesizesizesize and shapeshapeshapeshape. Corresponding angles and corresponding sides are in the same position in polygons with the same number of sides.

Two or more polygons whose corresponding angles and sides are congruent. In a congruence statement, the order of the vertices indicates the corresponding parts.

Example: Name the corresponding angles if polygon SWIM ≅ polygon ZERO.

∠S ≅ ∠Z; ∠W ≅ ∠E; ∠I ≅ ∠R; ∠M ≅ ∠O

Example

E D

R P

A

C

Corresponding Angles

∠R ≅ ∠C

∠E ≅ ∠P

∠D ≅ ∠A

Corresponding Sides

≅RD CA

≅ED PA

≅RE CP

Thus, ΔRED ≅ ΔCPA.

Side-Side-Side Congruence Postulate

If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.

T

I

N

C

U

P

4

6

7 4

6

7

ΔTIN ≅ ΔCUP

Example Given: , D is the midpoint of

Prove: ∆FRD ≅ ∆ERD

F

R

ED

FR ER≅ FE

StatementsStatementsStatementsStatements ReasonsReasonsReasonsReasons

1. 1. Given

2. D is midpt of 2. Given

3. 3. Def. of midpoint

4. 4. Refl. prop. ≅

5. ∆FRD ≅ ∆ERD 5. SSS

FR ER≅

FE

FD ED≅

RD RD≅

Side-Angle-Side Congruence Theorem

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

L

H

S

U

T

A

ΔLHS ≅ ΔUTA

Example Given: , A is the midpoint of

Prove: ∆FAR ≅ ∆EAM F

R

AM

E

FA EA≅ RM

StatementsStatementsStatementsStatements ReasonsReasonsReasonsReasons

1. 1. Given

2. ∠FAR ≅ ∠EAM 2. Vertical ∠s

3. A is midpt of 3. Given

4. 4. Def. of midpoint

5. ∆FAR ≅ ∆EAM 5. SAS

FA EA≅

RM

RA MA≅