Chapter 1 Test Tuesday, August 29th Chapter 1 Student Notes Chapter 1 Test Tuesday, August 29th

1.1 Points, Lines and Planes

Point - A B

Line - C D m

Collinear - T / F A and B are Collinear T / F A and C are Collinear A B C T / F A and B are Collinear T / F A and C are Collinear T / F A, B and C are Collinear

Plane - A B C P

Coplanar - Name 3 Coplanar Points ________ Name 3 Noncoplanar Points _________ T/F C, D and G are coplanar T/F A, B, E, F are coplanar T/F A, B, C, E are coplanar A B C D G E F

Draw and Label each of the following n and m intersect at P p contains N P contains A and B, but not C

Draw and Label each of the following 4. m intersects P at X 5. P and R intersect at m

1.2 Segments Objective: Learn the language of Geometry Become familiar with segments and segment measure

Line Segment - A B

Betweenness of Points - A B C

Measure of a Segment - M 6 N

Segment Congruence - R 7 T S 7 U

Segment Congruence is marked on a figure in the following manner. 12 12 B C

Multiple Pairs of Congruent Segments D From the markings on the above figure, make 2 congruence statement. B C

A is between C and D. Find Each Measure. AC = 4, AD = 3, Find CD = ______ CD = 15, AD = 7, Find AC = _____ C 4 A 3 D C A 7 D 15

A is between C and D. Find Each Measure. 3. AC = x + 1, AD = x + 3, CD = 3x – 5, Find x = _____ C x + 1 A x + 3 D 3x - 5

A is between C and D. Find Each Measure. AC = 8, AD = 5, Find CD = ______ CD = 20, AD = 12, Find AC = _____ C 8 A 5 D C A 12 D 20

A is between C and D. Find Each Measure. 3. AC = 2x + 1, AD = 2x + 3, CD = 5x – 10, Find x = ___ C 2x + 1 A 2x + 3 D 5x – 10

C is between A and B in each figure. Select the figure that has AB = 12. Select all that apply. A. C is between A and B. B. B is between A and D. A 8 C 4 B D 8 B A B is between A and D. AB = 2x + 5, BD = 3x + 4, AD = 6x – 3 B is between A and D. AB = 2x + 2, DB = 4x +2, DA =34 D B A D B A Answer: ____________

1.3 Distance and Midpoint

Distance on a Number Line = Use the number line to find the length of each segment. A B C D -5 0 5 AB = BC = AD = BD =

Distance on a Coordinate Plane Formula Find the length of each segment. AB = A(2, 2) B(-4, 1) C(2, -4)

Find the length of each segment. BC A(2, 2) B(-4, 1) C(2, -4)

Midpoint on a Number Line A B C D -5 0 5 Find the midpoint of each segment. 1. AB 2. AD

Find the midpoint of each segment. A B C D -5 0 5 3. BC If A is the midpoint of EC, what is the location for point E?

Midpoint on a Coordinate Plane x1 + x2 , y1 + y2 2 2 A(2, 2) Find the midpoint of each segment. 1. AB B(-4, 1) = ( ) = ( ) C(2, -4)

Midpoint on a Coordinate Plane Find the midpoint of each segment. 1. BC = ( ) A(2, 2) = ( ) B(-4, 1) C(2, -4)

Midpoint on a Coordinate Plane Find the midpoint of each segment. 2. AC = ( ) A(2, 2) = ( ) B(-4, 1) C(2, -4)

M is the midpoint of AB. Given the following information, find the missing coordinates. x1 + x2 , y1 + y2 2 2 M(2, 6) , B(12, 10) , A ( ? , ? )

M is the midpoint of AB. Given the following information, find the missing coordinates. x1 + x2 , y1 + y2 2 2 M(6, -8) , A(2, 0) , B ( ? , ? )

1.4 Angle Measure

Ray - R B A D S E

Angle–

Points _______________________________ G ____________________ Angles and Points Points _______________________________ G ____________________ H ____________________ E ____________________ D G H F E

________ Naming Angles D G H F 2 E Name the angle at the right as many ways as possible. ________ D G H F 2 E

Naming Angles _______ _______ J M L 3 2 K Name the angles at the right as many ways as possible. _______ _______ J M L 3 2 K

Naming Angles _________ J M L 3 2 K Name the angles at the right as many ways as possible. _________ J M L 3 2 There is more than one angle at vertex K, K ● __________________ ____________________________________ ●

________ different types of angles: Right angle: Acute angle:

Can also be called __________ ________________. Types of Angles Obtuse angle: Straight angle: Can also be called __________ ________________.

Congruent Angles 33o W M 33o

Multiple Sets of Congruent Angles B __________ C D

Angle Bisector _________________ or ________________ KM is an angle bisector. What conclusion can you draw about the figure at the right? J M _________________ or ________________ 4 L 6 K

_____________________________. Adding Angles 4/21/2017 When you want to add angles, use ______________________ _____________________________________________________________.. If you add m1 + m2, what is your result? _____________________________. J M 48o 28o L 1 2 ● K

Angle Addition Postulate The sum of the two smaller angles adjacent angles will _______________________________________________________________________________________________. R U 1 T 2 Complete: m ______ + m  ______ = m  _______ or S

Example Draw your own diagram and answer this question: If ML is an angle bisector of PMY and mPML = 87, then find: mPMY = _______ mLMY = _______

JK is an angle bisector of LJM. mLJK = 4x + 10, mKJM = 6x – 4 JK is an angle bisector of LJM. mLJK = 4x + 10, mKJM = 6x – 4. Find x and mLJM. L (4x + 10)o K (6x – 4)o J M mLJM = _____

RS is an angle bisector of PRT. mPRT = 11x – 12, mSRT = 4x + 3 RS is an angle bisector of PRT. mPRT = 11x – 12, mSRT = 4x + 3. Find x and mPRS. P S (4x + 3)o R T mPRS = ___

1-5 Angle Pairs

Complementary Angles - Examples: M R D 1 2 N S T Perpendicular – _______________________

Supplementary Angles- Examples: G L 2 1 H J K K

Adjacent Angles

Adjacent Angles 3 4

Vertical Angles- Example: C A 3 2 1 E 4 B D

Theorem: C ● A 3 2 1 E 4 D B

What’s “Important” in Geometry? 4 things to always look for ! Most of the rules (theorems) and vocabulary of Geometry are based on these 4 things. . . . and ___________( )

Examples 1 & 2 are complementary. m1 = 4x + 5, m2 = 5x + 4. Find x and the measure of each angle. x = _____ m1 = _____ m2 = _____

Examples 5 & 6 are supplementary. m5 = 10x + 12, m6 = 2x + 6. Find x and the measure of each angle. x = _____ m5 = _____ m6 = _____

Examples 2 1 3 4 m1 = 2x + 7, m3 = 3x – 3. Find x and the measure of each angle. Find x = _____ m 2 = _____ m1 = _____

Examples 2 1 3 4 m2 = 5x + 12, m4 = 7x – 20. Find x and the measure of each angle. x = _____ m 2 = _____ m1 = _____

1.6 Polygons

Determine if each figure is a polgyon Polygon - Determine if each figure is a polgyon

Concave Polgons Example of Concave Polygons

Convex Polygons Examples of Convex Polygons

Number of Sides 3 4 5 6 7 8 9 10 11 12 13 n Name of Polygon Hint

Regular Polygon- Examples of Regular Polygons

distance around a polygon Perimeter - distance around a polygon Find the perimeter of each polygon. Regular Hexagon Rectangle Square 3cm 4ft 8in 6cm P = _______ P = ________ P = ______

Name each polygon by its number of sides Name each polygon by its number of sides. Then classify it as concave or convex and regular or irregular.

Name each polygon by its number of sides Name each polygon by its number of sides. Then classify it as concave or convex and regular or irregular.

Find the perimeter and area of the polygon below. 8cm P = ________ 3cm 5cm 5cm 5cm A = ________ 5cm 3cm 8cm

Triangle ABC has the following coordinates. Find the perimeter of ABC.