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Warm-Up - Artists Vito Acconci is a popular American sculptor and artist. One of his furniture creations called the Name Calling Chair uses a variety of geometric shapes, such as squares and triangles. The back of the chair is shown in the diagram. • What do you know about angles FCB and CFE? Are triangles ABC and DEF similar? • Are triangles ABC and DEF congruent?

Congruent Triangles – Day 2

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Page 1: Congruent Triangles – Day 2

Warm-Up - Artists• Vito Acconci is a

popular American sculptor and artist. One of his furniture creations called the Name Calling Chair uses a variety of geometric shapes, such as squares and triangles. The back of the chair is shown in the diagram.

• What do you know about angles FCB and CFE?• Are triangles ABC and DEF similar?• Are triangles ABC and DEF congruent?

Page 2: Congruent Triangles – Day 2

Congruent Triangles – Day 2Congruence & Triangles

Page 3: Congruent Triangles – Day 2

Congruent Figures

•Exact same shape•Exact same size

Congruent Not Congruent

Page 4: Congruent Triangles – Day 2

Properties of Congruent Figures

•Corresponding Angles are Congruent•Corresponding Sides are congruent

PQRABC

A

B

C

P

QR

Page 5: Congruent Triangles – Day 2

Example 1: Write a congruence statement and identify all corresponding parts.

X

Y

Z

H

K

J

Page 6: Congruent Triangles – Day 2

Example 2: ABCD KJHL

a.Find the value of x

b. Find the value of y

A

B

C

D

K

J

H

L

91 8

6

9 cm

6 cm(4x – 3) cm

(2y – 4) o

Page 7: Congruent Triangles – Day 2

Third Angles Theorem

•If 2 angles in a triangle are congruent to 2 angles in a 2nd triangle, then the 3rd angles are also congruent.

A

B

C

D

E

F

Page 8: Congruent Triangles – Day 2

Example 3: Find the value of x

A

B

C

D

E

F

22o

87o

(4x+15)o

Page 9: Congruent Triangles – Day 2

Find the value of the variables.

Page 10: Congruent Triangles – Day 2

Find the value of the variables.

Page 11: Congruent Triangles – Day 2

Decide whether the triangles are congruent. Justify reasoning.

E

F

G

H

J

58o

58o

Page 12: Congruent Triangles – Day 2

Are there any congruent figures?If so, what is the congruence statement?

Page 13: Congruent Triangles – Day 2

Are there any congruent figures?If so, what is the congruence statement?

Page 14: Congruent Triangles – Day 2

Are there any congruent figures?If so, what is the congruence statement?

Page 15: Congruent Triangles – Day 2

Homework – Day 2

Page 16: Congruent Triangles – Day 2

4.1/4.2 Practice

Page 17: Congruent Triangles – Day 2
Page 18: Congruent Triangles – Day 2