1. Lesson 1-R
Chapter Review

2. Lesson Outline Five-Minute Check Objectives Vocabulary Core Concepts
Examples
Summary and Homework

3. 5-Minute Check on Lesson 1-6
𝑩𝑫 bisects ABC. Use the diagram and the given angles to answer.
mABD = 57°. Find mDBC and mABC.
mABC = 110°. Find mDBC and mABD.
B is supplement of A and mA = 65°. Find mB
C is complement of A and mA = 60°. Find mC
D is a linear pair with A and mA = 55°. Find mD
E is vertical with A and mA = 45°. Find mE
mDBC = 57° and mABC = 114°
mDBC = 55° and mABD = 55°
mB + mA = 180° – 65 = 115° = mB
mB + mA = 90° – 60 = 30° = mC
mD + mA = 180° – 55 = 125° = mD
mE = mA = mE

4. Objectives
Review chapter one material and vocabulary

5. Vocabulary none new Must know the terms from chapter 1 !!!
Complementary versus supplementary
Linear pairs versus vertical angles
Concave versus convex
Regular versus irregular
Schwarzwaldekirchekȕchen means what?

6. Visual Definitions k Points A, B, C, D Line k Collinear A, B, Cy
A, B, C, D
Line k
(-5,5) k
(6,4) D C
Collinear
(0,1)
A, B, C x A
Line Segments
(-6,-2)
BA, BC, AC B
Plane
xy coordinate
Coplanar
A, B, C, D

7. Whole = Sum of its Parts
Any distance (or angle) can be broken into pieces and the sum of those pieces is equal to the whole distance (or measure of an angle) 11 14 6 A B C D 31
The whole length, AD, is equal to the sum of its parts, AB + BC + CD
AD = AB + BC + CD
31 =

8. Distance Review Concept Formula Examples Distance Nr line Coord Plane
D = | a – b |
D = | 2 – 8| = 6
D = (x2-x1)2 + (y2-y1)2
D = (7-1)2 + (4-2)2 = 40 a b 2 3 4 5 6 7 8 9 1
(1,2)
(7,4) Y X ∆x ∆y D
Pythagorean Theorem on the formula sheet !!

9. Mid-points Review Concept Formula Examples Mid point Nr line
Coord Plane
(a + b) 2
(2 + 8) 2
[x2+x1] , [y2+y1]
7 + 1 ,
= 5
= (4, 3) a b 2 3 4 5 6 7 8 9 1
(1,2)
(7,4) Y X M
Given an endpoint and the midpoint is a “travel” problem
Endpoint: (1, 2)
Midpoint: (4, 3)
By equations:
Midpoint (4, 3) Midpoint (4, 3)
̶ Endpoint (1, 2) Travel (3, 1)
Travel (3, 1) Other End (7, 4)
By graphing: 3 right and 1 up to get to the middle. Have to go same distance to get to the other end.

10. Interior of angle AVB or V
Angles
360º A
Circle
Exterior of angle
Ray VA
Interior of angle AVB or V
Vertex (point V) V
Ray VB B
Angles measured in degrees
A degree is 1/360th around a circle
Acute
Right
Obtuse A A A
mA < 90º
mA = 90º
90º < mA < 180º
Names of angles: Angles have 3 letter names (letter on one side, letter of the vertex, letter on the other side) like AVB or if there is no confusion, like in most triangles, then an angle can be called by its vertex, V

11. Angle Vocabulary
Linear pair – a pair of adjacent angles whose noncommon sides are opposite rays (always supplementary)
Vertical angles – two non adjacent angles formed by two intersecting lines. Vertical angles are congruent (measures are equal)!!
Complementary Angles – two angles whose measures sum to 90°
Supplementary Angles – two angles whose measures sum to 180°
Perpendicular – two lines or rays are perpendicular if the angle (s) formed measure 90°

12. Figures Vocabulary Number of Sides Polygon Name 3 Triangle 4
Quadrilateral 5
Pentagon 6
Hexagon 7
Heptagon 8
Octagon 9
Nonagon 10
Decagon 12
Dodecagon n
N-gon
Concave – figure has an interior angle greater than 180
Convex – no sides “extended” pass through the interior of the figure
Regular – all sides equal and all angles equal in a figure
Irregular – sides or angles are different measures in a figure
Perimeter – all sides of a figure added up
Area – the “square units” of a figure’s interior

13. Summary & Homework Summary: Homework: Vocabulary is very important
SOL topics:
Distance formula
Midpoints (regular and travel problems)
Special angle pairs
Complementary and supplementary
Homework:
study for the quiz

14. Vocabulary Important Complementary versus Supplementary Perpendicular
Collinear versus Coplanar
Perimeter
Adjacent angles
Vertical angles versus Linear Pairs
Congruent Segments and Angles
Concave versus Convex
Regular versus Irregular
Bisector (angle or segment)

15. Symbols are like Vocabulary
What do the following symbols mean?    
Congruent Segments
Congruent
Angles
Right Angle
m = 90
Angle
Bisector
Ray
Line Segment
Line
Congruent
Angle
Perpendicular
Equal

16. Finding Angles Information
Once around a point is 360
Linear Pairs are supplementary
Sum of triangle’s angles is 180
Vertical angles are congruent
3 = 151
5 = 151
4 = 29
6 = 29
12 = 42
10 = 42
11 = 138
9 = 138
7 = 109
1 = 109
2 = 71
8 = 71 1 2 3 4 5 6 7 8 10 11 9 12
If 3 = 151 and 12 = 42, find the rest

17. Finding Distance
Distance formula and Pythagorean theorem are very similar
Either can be used; formula must be memorized, but theorem is on formula sheet
Given: A (2, 4) and B (5, 8),
find the length of AB y x
a = 5 – 2 = 3 b = 8 – 4 = 4
d = (a)2 + (b)2
d = (3)2 + (4)2 = (9) + (16) =  25 = 5
Given: C (-1, -4) and D (-5, -4),
find the length of CD
d = (-1 – (-5))2 + (-4 – (-4))2
d = (4)2 + (0)2
d = (16) = 4

18. Finding Midpoints Midpoint formula must be memorized Two problem types
Given two endpoints, find the midpoint
Given endpoint and midpoint, find the other endpoint
Given: A (2, 4) and B (5, 8),
find the midpoint of AB
Given: A (-3, -5) and the midpoint of AB is (1, -1),
find B
x: (2+5)/2 = 7/2 = 3.5
y: (4+8)/2 = 12/2 = 6
Midpoint (3.5, 6)
MP (1, -1)
- EP (-3, -5)
Travel (+4, +4)
+ MP (1, -1)
OEP (5, )
Travel -3 to 1 is + 4
-5 to -1 is + 4

19. Miscellaneous Perimeter is once around the figure; add up the sides
Equations are the language of Math
Any geometry problem can be turned into an algebra problem D A A D C B B C
CAB = 2x – 6 , CAD = x + 8,
Find x and BAD
AB = 2x, AD = 2x + 8, BC = 3x – 2
Find x and perimeter
2x – 6 = x so x = 14
BAD = CAB + CAD = 3x + 2
= 3(14) + 2 = 44
P = 2x + 2x x + 3x – 2 = 9x + 6 = 96
2x + 8 = 3x – 2 so x = 10