Warm Up

What is a segment bisector?

What is an angle bisector?

Return of the Quizzes

Retakes

• Deadlines are on the board in the back!!!!

OBJECTIVE:

WHAT DOES CONGRUENT

MEAN???

Rigid Motions

• What are Rigid Motions???

• “Motions that preserve the size and shape of figures”

• Who can name some Rigid Motions that we know???

• Translations

• Rotations

• Reflections

Congruent = same size, same shape

• What do we mean by same shape?

• All the angles are the same

• What do we mean by same size?

• All the side lengths are the same

Two Congruent Triangles…

If I tell you that triangle CAT is congruent to triangle DOG…

what else can you conclude? Tell me everything you know!

C

A T D

O G

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

Helpful Hint

Given: ∆PQR ∆STW Identify all pairs of corresponding congruent parts.

Angles: P S, Q T, R W

Sides: PQ ST, QR TW, PR SW

If polygon LMNP polygon EFGH, identify all pairs of corresponding congruent parts.

Angles: L E, M F, N G, P H

Sides: LM EF, MN FG, NP GH, LP EH

Two Congruent Quadrilaterals

M A

T H

S F

U N

Given: ∆ABC ∆DEF

Find the value of x.

2x – 2 = 6

2x = 8

x = 4

AB DE

AB = DE

x = 21

y = 6

z = 6

Given: EFG RST. Find the values of x, y, and z.

Given: CDE HIJ, DE 9x,

and IJ 7x + 3. Find x and DE.

Given: CDE HIJ, mD (5y + 1) ,

and mI (6y 25) .

Find y and mD.

y 26; mD 131

Solve the equation 4m – 8 = –12. Write a justification for each step.

4m – 8 = –12 Given equation

+8 +8 Addition Property of Equality

4m = –4 Simplify.

m = –1 Simplify.

Division Property of Equality

Solve for x. Write a justification for each step.

NO = NM + MO

4x – 4 = 2x + (3x – 9) Substitution Property of Equality

Segment Addition Post.

4x – 4 = 5x – 9 Simplify.

–4 = x – 9

5 = x Addition Property of Equality

Subtraction Property of Equality

Solve for x.

Write a justification for each step.

x = 11

Subst. Prop. of Equality 8x° = (3x + 5)° + (6x – 16)° 8x = 9x – 11 Simplify.

–x = –11 Subtr. Prop. of Equality.

Mult. Prop. of Equality.

Add. Post. mABC = mABD + mDBC

What do we KNOW?

What are we trying to prove?

What do we KNOW?

What are we trying to prove?