Warm Up 11.03.11Week 3

Tell whether it is possible to draw each triangle:

1) right isosceles triangle

2) scalene equiangular triangle

3) right scalene triangle

Geometry

4.2 Day 2

I will identify congruent figures and corresponding parts.

Congruent Statement

Ex 1

A sentence or math expression expressing that two shapes are congruent.

∠A B because ≅ ∠they are equal to each other.38⁰ 38⁰

BA

C

E F

Ex 2∠E F because ≅ ∠they are vertical angles.

Congruent StatementShape

Ex 1 Prove both angles are congruent:

62º

62º

N

MP

R

Q

≅ ,

≅ ≅ ,

.

2) P N∠ ≅ ∠

3) NQM ∠ ≅PQR∠

4) R M∠ ≅ ∠

because they are both equal: 62º.

because they are vertical angles.

because of the third angle theorem.

1)

5) ∆PQR ≅ ∆NQM because of the definition of congruent triangles.

Theorem 4.4 Properties of Congruent Triangles

REFLEXIVE: Every triangle is congruent to itself.

 SYMMETRIC: If ∆ ABC ≅ ∆ DEF, then ∆ DEF ≅ ∆ ABC.

 TRANSITIVE: if ∆ ABC ≅ ∆ DEF and ∆ DEF ≅ ∆ JKL,

then ∆ABC ≅ ∆JKL.

A

B

C D

E

F J

K

L

A

B

C D

E

F40

º

80º5m

º

Given: A ∠ ≅ D and B ∠ ∠ ≅ E,∠ find the value of m.

1) B ∠ ≅ E so ∠ m B ∠ = m E. ∠

2) m B ∠ = 80º because B ∠ is equal to E. ∠

3) m C = 60º because of T4.1.∠

4) 60º = 5mº because of T4.3.

5) 12 = m

Do: 1

Assignment:

Textbook Page 207, 24 - 32 all.

What is the m∠R and the value of x?

72º

N

MP

R

Q42º

4xº