1-3 Measuring and constructing angles Chapter 1 1-3 Measuring and constructing angles

Warm up Instructions: Answer the following questions P1. M is between N and O. MO = 15, and MN = 7.6. Find NO. P2. S is the midpoint of TV, TS = 4x – 7, and SV = 5x – 15. Find TS, SV, and TV. P3. LH bisects GK at M. GM = 2x + 6, and GK = 24. Find x.

Warm up Answers Instructions: Answer the following questions P1. M is between N and O. MO = 15, and MN = 7.6. Find NO. Answer: 22.6 P2. S is the midpoint of TV, TS = 4x – 7, and SV = 5x – 15. Find TS, SV, and TV. Answer: 25,25,50 P3. LH bisects GK at M. GM = 2x + 6, and GK = 24. Find x. Answer: x=3

Objectives The students will be able to: * Name and classify angles. *Measure and construct angles and angle bisectors.

1-3 Measuring and constructing Angles What is an angle? Answer: is a figure formed by two rays, or sides, with a common endpoint called the vertex (plural: vertices). How can we name an angle? Answer: You can name an angle several ways: by its vertex, by a point on each ray and the vertex, or by a number.

1-3 measuring and constructing angles The set of all points between the sides of the angle is the interior of an angle. The exterior of an angle is the set of all points outside the angle. Examples of naming angles can be: Angle Name R, SRT, TRS, or 1

1-3 measuring and constructing angles Example 1: A surveyor recorded the angles formed by a transit (point A) and three distant points, B, C, and D. Name three of the angles. Answer:BAC, CAD, BAD

1-3 measuring and constructing angles Example 2: Name the following angles in three different ways

1-3 measuring and constructing angles The measure of an angle is usually given in degrees. Since there are 360° in a circle, one degree is 1/360 of a circle. When you use a protractor to measure angles, you are applying the following postulate:

1-3 Measuring and constructing angles You can use the Protractor Postulate to help you classify angles by their measure. The measure of an angle is the absolute value of the difference of the real numbers that the rays correspond with on a protractor. If OC corresponds with c and OD corresponds with d, mDOC = |d – c| or |c – d|.

1-3 measuring and constructing angles Example 3: Example problem types 1.  Measure the following angles.  If necessary, continue the sides of the angle..                             

1-3 measuring AND CONSTRUCTING ANGLES Example 3: Measuring angles online Measuring Angles with a Protractor - Welcome to Math Playground www.mathplayground.com/measuringangles.html

1-3 measuring and constructing angles

1-3 measuring and constructing angles Example 5: Find the measure of each angle. Then classify each as acute, right, or obtuse. A. WXV mWXV =180-150= 30° WXV is acute. B. ZXW mZXW = |130° - 30°| = 100 ZXW = is obtuse

1-3 measuring and constructing angles What are congruent angles? Congruent angles are angles that have the same measure. In the diagram, mABC = mDEF, so you can write ABC  DEF. This is read as “angle ABC is congruent to angle DEF.” Arc marks are used to show that the two angles are congruent.

1-3 measuring and constructing angles

1-3 measuring and constructing angles Example 6: Problem 1 from the angle addition postulate worksheet 1) Find 𝑚<𝐾𝐿𝑀 if 𝑚<𝐾𝐿𝐵 = 26° and 𝑚<𝐵𝐿𝑀 = 60°. Solution: 𝑚<𝐾𝐿𝑀=𝑚<𝐾𝐿𝐵+𝑚<𝐵𝐿𝑀 angle addition postulate 𝑚<𝐾𝐿𝑀=26+ 60 substitute values and simplify 𝑚<𝐾𝐿𝑀=86

1-3 measuring and constructing angles Example 7: Problem 8 from the angle addition postulate worksheet Find 𝑚<𝐼𝐻𝑄 if 𝑚<𝐼𝐻𝐺 = 176°and 𝑚<𝑄𝐻𝐺 = 130°. Solution: 𝒎<𝑰𝑯𝑮=𝒎<𝑰𝑯𝑸+𝒎<𝑸𝑯𝑮 angle addition 176=x+130 substitute values and solve -130 -130 46=x

1-3 measuring and constructing angles Example 8 Problem 11 from the angle addition postulate worksheet ) 𝑚<𝐻𝐺𝐹 =16𝑥+ 4, 𝑚<𝐸𝐺𝐹 = 110°,and 𝑚<𝐻𝐺𝐸 =3𝑥+11. Find x. Solution 𝑚<𝐻𝐺𝐹=𝑚<𝐸𝐺𝐹+𝐻𝐺𝐸 angle addition postulate 16𝑥+4=110+ 3𝑥+11 substitute vales and simplify 16𝑥+4=3𝑥+121 simplify −3𝑥−4=−3𝑥−4 solve for x 13𝑥 13 = 117 13 X=9

1-3 measuring and constructing angles What is an angle bisector ? Solution: An angle bisector is a ray that divides an angle into two congruent angles. JK bisects LJM; thus LJK  KJM.

1-3 measuring and constructing angles Example 9 Problem 13 from the angle bisector worksheet Find x if 𝑚<2 =4𝑥+ 5 and 𝑚<1 =5𝑥− 2. Solution 𝑚<1=𝑚<2 angle bisector 5𝑥−2=4𝑥+5 simplify and solve for x −4𝑥+2 −4𝑥+2 X=7

Student guided practice Do worksheet A Do Worksheet B 2-8

Homework Do problems 2-10 in your book page 24

Closure Today we learned about naming and measuring the angles. We also learned about the angle addition postulate and the angle bisector. Tomorrow we are going to continue with lesson 1-4.