congruent triangles an introduction to corresponding parts

Congruent Triangles

An Introduction to Corresponding Parts

Two figures are congruent if they are the same size and same shape.

∆ABC is congruent to ∆XYZ

A B

C

X Y

Z

∆ABC is congruent to ∆XYZ

A B

C

X Y

Z

Corresponding parts of these triangles are congruent.

∆ABC is congruent to ∆XYZ

A B

C

X Y

Z

Corresponding parts of these triangles are congruent.

Corresponding parts are angles and sides that “match.”

∆ABC is congruent to ∆XYZ

A B

C

X Y

Z

Corresponding parts of these triangles are congruent.

A X

∆ABC is congruent to ∆XYZ

A B

C

X Y

Z

Corresponding parts of these triangles are congruent.

B Y

∆ABC is congruent to ∆XYZ

A B

C

X Y

Z

Corresponding parts of these triangles are congruent.

C Z

∆ABC is congruent to ∆XYZ

A B

C

X Y

Z

Corresponding parts of these triangles are congruent.

AB XY

∆ABC is congruent to ∆XYZ

A B

C

X Y

Z

Corresponding parts of these triangles are congruent.

BC YZ

∆ABC is congruent to ∆XYZ

A B

C

X Y

Z

Corresponding parts of these triangles are congruent.

AC XZ

∆BAD is congruent to ∆THE

B A

D E

T H

Name all corresponding parts.

∆QRS is congruent to ∆BRX

BR

Q

S

X

Name all corresponding parts.

∆EFG is congruent to ∆HFG

H

G

F

E

Name all corresponding parts.

15

Using Corresponding PartsIn the diagram, ΔITP ≅ ΔNGO. Find the values of x and y.

In the figure, quadrilateral JIHK quadrilateral QRST.

Find a.

3a

4b° 6

30°Q

120°R S

H I

J

K c + 10°

T

In the figure, quadrilateral JIHK quadrilateral QRST.

3a

4b° 6

30°Q

120°R S

H I

J

K c + 10°

T

Find b.

In the figure, quadrilateral JIHK quadrilateral QRST.

Find c.

3a

4b° 6

30°Q

120°R S

H I

J

K c + 10°

T

19

Prove That Two Triangles are CongruentWrite a two-column proof.

Prove: ΔLMN ≅ ΔPON

Statements Reasons

Find the missing information in the following proof.

Prove: ΔQNP ≅ ΔOPN

Proof:ReasonsStatements

3. Given3.∠Q ≅ ∠O, ∠NPQ ≅ ∠PNO

2. 2. Reflexive Property of Congruence

5. Definition of Congruent Polygons5. ΔQNP ≅ ΔOPN

4. _________________4. ∠QNP ≅ ∠ONP ?

1. 1. Given

22

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Homework!!

• Pg. 257 (4 - 20, 24, 28 - 30)