entry task if ydf = 121 and dr bisects fdi find the measure of: a) ida b) yda c) rdi y d a f r i

Entry Task

If ∠ YDF = 121 and DR bisects ∠FDI find the measure of:a) ∠ IDAb) ∠ YDAc) ∠ RDI

Y

D

A

F

R

I

Properties of Parallel Lines3.2

Learning Target: I can use parallel lines to prove angle relationships

Success Criteria:

I can find the measures of angles formed by parallel lines crossed by a transversal.

I can prove angles congruent using the theorems and properties of parallel lines crossed by a transversal

Parallel Lines

• Using the 2 parallel lines, draw a transversal that intersects both lines.

• Predict, based on visual inspection connections about angle pairs– Corresponding– Alternate Exterior– Alternate Interior– Same Side Interior Angles

• Compare your findings with your table partners• Measure all 8 angles using a protractor• On your paper, compare your predictions to your

measurements

Parallel Lines Cont…..

• Make a general statement about each angle pair• Share with your table partner each of the four

statements• Assign an angle pair to each student• Move to correct corner of room and share with

new group• Create a General Statement on an 8x11 piece of

paper for our Public Record

Proving Lines Parallel• Watch this Video first

• Then watch this Video

Check It Out! Example 1

Find mQRS.

mQRS = 180° – x

x = 118

mQRS + x = 180°

Corr. s Post.

= 180° – 118°

= 62°

Subtract x from both sides.

Substitute 118° for x.

Def. of Linear Pair

Find each angle measure.

Example 2: Using the Corresponding Angles Postulate

A. mECF

x = 70

B. mDCE

mECF = 70°

Corr. s Post.

5x = 4x + 22 Corr. s Post.

x = 22 Subtract 4x from both sides.

mDCE = 5x

= 5(22) Substitute 22 for x.

= 110°

Find each angle measure.

Example 3: Finding Angle Measures

A. mEDG

B. mBDG

mEDG = 75° Alt. Ext. s Thm.

mBDG = 105°

x – 30° = 75° Alt. Ext. s Thm.

x = 105 Add 30 to both sides.

Check It Out! Example 4

Find mABD.

mABD = 2(25) + 10 = 60°

2x + 10° = 3x – 15° Alt. Int. s Thm.

Subtract 2x and add 15 to both sides.x = 25

Substitute 25 for x.

Same as #1

Homework

• Homework P. 153 #7-10, 12-20,22

• Challenge - 28