# 7-1 points, lines, planes, and angles course 3 warm up warm up problem of the day problem of the day...

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7-1 Points, Lines, Planes, and AnglesCourse 3Warm UpProblem of the DayLesson Presentation

Warm UpSolve.

1. x + 30 = 90

2. 103 + x = 180

3. 32 + x = 180

4. 90 = 61 + x

5. x + 20 = 90x = 60x = 77x = 148x = 29x = 70

Problem of the Day Mrs. Meyers class is having a pizza party. Half the class wants pepperoni on the pizza, of the class wants sausage on the pizza, and the rest want only cheese on the pizza. What fraction of Mrs. Meyers class wants just cheese on the pizza?

Learn to classify and name figures.

Vocabularypointlineplanesegmentrayangleright angleacute angleobtuse anglecomplementary anglessupplementary anglesvertical anglescongruentInsert Lesson Title Here

Points, lines, and planes are the building blocks of geometry. Segments, rays, and angles are defined in terms of these basic figures.

A point names a location. APoint A

A line is perfectly straight and extends forever in both directions.

A plane is a perfectly flat surface that extends forever in all directions.plane P, or plane DEFDEFP

GHA segment, or line segment, is the part of a line between two points.

KJA ray is a part of a line that starts at one point and extends forever in one direction. KJ

Additional Example 1: Naming Points, Lines, Planes, Segments, and RaysA. Name 4 points in the figure.B. Name a line in the figure.Point J, point K, point L, and point MAny 2 points on a line can be used.

Additional Example 1: Naming Points, Lines, Planes, Segments, and Rays C. Name a plane in the figure.Any 3 points in the plane that form a triangle can be used.

Additional Example 1: Naming Points, Lines, Planes, Segments, and Rays D. Name four segments in the figure.E. Name four rays in the figure.

Check It Out: Example 1A. Name 4 points in the figure.B. Name a line in the figure.Point A, point B, point C, and point DABCDAny 2 points on a line can be used.

C. Name a plane in the figure.Any 3 points in the plane that form a triangle can be used.ABCDCheck It Out: Example 1

D. Name four segments in the figureE. Name four rays in the figureABCDCheck It Out: Example 1

The measures of angles that fit together to form a straight line, such as FKG, GKH, and HKJ, add to 180.

The measures of angles that fit together to form a complete circle, such as MRN, NRP, PRQ, and QRM, add to 360.

A right angle measures 90. An acute angle measures less than 90. An obtuse angle measures greater than 90 and less than 180.Complementary angles have measures that add to 90. Supplementary angles have measures that add to 180.

Additional Example 2: Classifying AnglesA. Name a right angle in the figure.B. Name two acute angles in the figure.TQSTQP, RQS

Additional Example 2: Classifying AnglesC. Name two obtuse angles in the figure.SQP, RQT

Additional Example 2: Classifying AnglesD. Name a pair of complementary angles.TQP, RQSmTQP + m RQS = 47 + 43 = 90

Additional Example 2: Classifying AnglesE. Name two pairs of supplementary angles.TQP, RQTSQP, SQRmTQP + m RQT = 47 + 133 = 180mSQP + m SQR = 137 + 43 = 180

Check It Out: Example 2A. Name a right angle in the figure.BEC

C. Name two obtuse angles in the figure.BED, AECB. Name two acute angles in the figure.AEB, CEDCheck It Out: Example 2

D. Name a pair of complementary angles.AEB, CEDCheck It Out: Example 2mAEB + m CED = 15 + 75 = 90

E. Name two pairs of supplementary angles.AEB, BEDCED, AECCheck It Out: Example 2mAEB + mBED = 15 + 165 = 180mCED + mAEC = 75 + 105 = 180

Congruent figures have the same size and shape. Segments that have the same length are congruent. Angles that have the same measure are congruent. The symbol for congruence is , which is read is congruent to.Intersecting lines form two pairs of vertical angles. Vertical angles are always congruent, as shown in the next example.

Additional Example 3A: Finding the Measure of Vertical AnglesIn the figure, 1 and 3 are vertical angles, and 2 and 4 are vertical angles.If m1 = 37, find m 3.The measures of 1 and 2 are supplementary.The measures of 2 and 3 are supplementary.m2 = 180 37 = 143m3 = 180 143 = 37

Additional Example 3B: Finding the Measure of Vertical AnglesIn the figure, 1 and 3 are vertical angles, and 2 and 4 are vertical angles.If m4 = y, find m2.m3 = 180 ym2 = 180 (180 y)= 180 180 + y= yDistributive Property m2 = m4

In the figure, 1 and 3 are vertical angles, and 2 and 4 are vertical angles.If m1 = 42, find m3.1234Check It Out: Example 3AThe measures of 1 and 2 are supplementary.The measures of 2 and 3 are supplementary.m2 = 180 42 = 138m3 = 180 138 = 42

In the figure, 1 and 3 are vertical angles, and 2 and 4 are vertical angles.If m4 = x, find m2.m3 = 180 xm2 = 180 (180 x)= 180 180 + x= xDistributive Property m2 = m4Check It Out: Example 3B1234

Lesson QuizIn the figure, 1 and 3 are vertical angles, and 2 and 4 are vertical angles.1. Name three points in the figure.3. Name a right angle in the figure.4. Name a pair of complementary angles.5. If m1 = 47, then find m 3.2. Name two lines in the figure.Possible answer: A, B, and CPossible answer: AGFPossible answer: 1 and 247