Suppose S is between R and T Suppose S is between R and T. Use the Segment Addition Postulate or sum of the parts = whole or the add two parts of a line together thing to solve for the variable. RS = 12, ST = 2x, RT = 34 1. RS = 16, ST = 2x, RT = 5x+10 2. 3. RS = 4y-1, ST = 2y-1, RT = 5y 4. RS = 2z+6, ST = 4z-3, RT = 5z+12

Find the value of the variable and PB, if P is between A and B. AP=-2s, PB=s+8, AB=11 1.

Lesson 1-4 Learners will be able to measure and classify angles, congruent angles, and angle bisectors.

A ray is a part of a line. It has one endpoint and extends indefinitely in one direction. Rays are named stating the endpoint first and then any other point on the ray.

If you choose a point on a line, you make exactly two rays called opposite rays. Z Y X Y Z Name the 2 Rays…

An angle is the intersection of two noncollinear rays at a common endpoint. The common endpoint is called the vertex, and the rays are the sides of the angle.

An angle can be named by a single letter… ex: B Or by three letters: a point on one side, the vertex, and a point on the other side.… ex: ABC

Name all angles that have B as a vertex. Answer: 5, 6, 7, and ABG Example 4-1a

Answer: and or are the sides of 5. Name the sides of 5. Answer: and or are the sides of 5. Example 4-1b

Write another name for 6. Answer: EBD, FBD, DBF, and DBE are other names for 6. Example 4-1c

a. Name all angles that have X as a vertex. b. Name the sides of 3. c. Write another name for 3. Answer: 1, 2, 3, and RXB or RXN Answer: Answer: AXB, AXN, NXA, BXA Example 4-1d

There is an interior and an exterior of an angle Z B C W Where is point Z? W? C?

Angles are measured in degrees. What are degrees? Da sun 1 of a circle 360

Logically where is a 45 angle? A right angle is an angle with a measurement of 90 Logically where is a 45 angle?

Obtuse: which have a measurement greater than 90 There are two other types of angles beside right angles…. 90 < mABC < 180 A C B Obtuse: which have a measurement greater than 90

Acute: which have a measurement lesser than 90 There are two other types of angles beside right angles…. A mABC < 90 C B Acute: which have a measurement lesser than 90

Measure TYV and classify it as right, acute, or obtuse. TYV is marked with a right angle symbol, so measuring is not necessary. Answer: is a right angle. Example 4-2a

Measure WYT and classify it as right, acute, or obtuse. Use a protractor to find that . Answer: > is an obtuse angle. Example 4-2b

Measure each angle named and classify it as right, acute, or obtuse. a. CZD b. CZE c. DZX Answer: 150, obtuse Answer: 90, right Answer: 30, acute Example 4-2d

Just like with congruent sides we also have congruent angles B

A ray or line that divides an angle into two congruent angles is called an angle bisector

A ray or line that divides an angle into two congruent angles is called an angle bisector

INTERIOR DESIGN Wall stickers of standard shapes are often used to provide a stimulating environment for a young child’s room. A five-pointed star sticker is shown with vertices labeled. Find mGBH and mHCI if GBH HCI, mGBH 2x + 5, and mHCI 3x – 10. Example 4-3a

Definition of congruent angles Given Definition of congruent angles Substitution Add 10 to each side. Subtract 2x from each side. Example 4-3b

Use the value of x to find the measure of one angle. Given or 35 Simplify. Since . Answer: Both measure 35. Example 4-3c

SIGNS A railroad crossing sign forms congruent angles SIGNS A railroad crossing sign forms congruent angles. In the figure, WVX ZVY. If mWVX 7a + 13 and mZVY 10a – 20, find the actual measurements of WVX and ZVY. Answer: Example 4-3d

Homework: Lesson 1-4, p. 33 # 4-36 even 42, 50