interactive powerpoint study guide for unit test 1 unit 1 review click here to go to the topics....
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CLICK TO EXPLORE UNIT 1
Unit 1 Objective
s
Naming and
Classifying
Divided Line
Segments
Divided Angles
Angle Relationship
sTriangles
Isosceles and
Equilateral
Properties
For SAT Practice, look on the CCSC website for the SAT PowerPoint from class.
For justification practice, look over notes, classwork, and homework.
You will be held responsible for everything in the Unit 1 Objectives. For topics not in this PowerPoint, look over notes, classwork, homework, do-
nows, and exit tickets.
name points, lines, line segments, rays, planes, angles, and triangles using names of points.
identify whether a set of given points is collinear. identify acute, obtuse, right, and straight angles
given a diagram or measurementsolve problems about congruent segments and
divided or bisected line segments.solve problems about congruent angles and divided
or bisected angles.solve problems about angle relationships, including
vertical and straight angles.use the fact that angles in a circle add up to 360 to
solve problems.determine the measurement of an angle that is
complementary or supplementary to a given angle.
YOU SHOULD BE ABLE TO…
There’s more!
determine the measurement of an angle that is complementary or supplementary to a given angle
use the triangle sum theorem to solve problems.Use the exterior angle theorem to solve problemsuse properties of angles in isosceles and equilateral
triangles to solve problems. use the “draw a picture and write in everything you
know” strategy to solve problems about angles in triangles.
write logical justifications to solutions to geometry problems using the following phrases “it is given that…” “Because [property]…” “Hence,…” and “Therefore [conclusion]”
solve SAT-type problems involving lines, angles, and triangles.
YOU SHOULD BE ABLE TO…
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NAMING AND CLASSIFYING OVERVIEW
Click each box to see the label and sketch for each geometric figure.
Point Line Line Segment
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NAMING AND CLASSIFYING OVERVIEW
Click each box to see the label and drawing for each geometric figure.
Ray Angle Triangle
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Next
*careful to label rays starting with the initial point.
*you should only label angles using one point if there are no other angles sharing the same vertex. Otherwise, use 3 points to label.
CLASSIFYING ANGLES
Click each box to see the definition and examples of each type of angle.
Acute Right
Obtuse Straight
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Try some Example
s
Angles that are greater than but less than
Angles that are equal to
Angles that are greater than but less than
Angles that are equal to
Use the figure shown to answer the problems.
CLASSIFYING EXAMPLES
1. List all of the angles that have S as a vertex.
2. Name a straight angle.
3. Name an obtuse angle.
4. Does appear to be obtuse, straight, right, or acute?
1. Show Answer
2. Show Answer
3. Show Answer
4. Show Answer
∠𝑇𝑆𝑈 ,∠𝑅𝑆𝑈 ,𝑎𝑛𝑑∠𝑅𝑆𝑇
∠𝑅𝑆𝑇
∠𝑇𝑆𝑈
Acute
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More Example
s
Name three collinear points shown in the diagram below.
CLASSIFYING EXAMPLES
Collinear Points:
Points that lie on the same line.
Show Answer
A, E, and Cor
D, E, and B
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Click each box to learn the vocabulary.
DIVIDED LINE SEGMENTS
congruent segments
bisects midpoint
two segments that have the same length.
divides a segment into two congruent segments
a point that bisects a segment
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DIVIDED LINE SEGMENTS
The Segment Addition Postulate:
If point B is between A and C, then AB+BC=AC.
Also,if AB+BC=AC, then point B is between A and C. AB + BC
= AC
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Try Some
Examples
If and , what is the length of ?
If and , what is the length of ?
DIVIDED SEGMENTS EXAMPLES
Note: Not drawn to scale.
Use the figure below to answer the questions.
Show Answer 𝐴𝐶=24
Show Answer 𝐵𝐶=16
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More Example
s
If , and , find .
If is two more than three times the length of and is 26, what is the length of ?
DIVIDED SEGMENTS EXAMPLES
Note: Not drawn to scale.
Use the figure below to answer the questions.
Show Answer 𝑥=16
Show Answer 𝐴𝐵=16
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More Example
s
is the midpoint of . If and , what is the length of
In parallelogram bisects and . If and what is the value of ?
DIVIDED SEGMENTS EXAMPLES
Show Answer 𝑋𝑍=4
Show Answer 𝑦=12
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DIVIDED ANGLES
Click each box to learn the vocabulary.
congruent angles
bisects bisector
two angles that have the same measure.
divides an angle into two congruent angles
a ray or segment that bisects an angle
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DIVIDED ANGLES
The Angle Addition Postulate:
If ray is on the interior of then .
Also,if then ray is on the interior of .
∠𝐴𝐵𝐷+¿
∠𝐷𝐵𝐶
¿∠𝐴𝐵𝐶Return to Main
Try Some
Examples
bisects If and then find the values of and the measure of all three angles ( and )
[Figure not drawn to scale]
DIVIDED ANGLES EXAMPLES
Show Answer ,
, Return to Main
ANGLE RELATIONSHIPS
Click each box to see the definition and examples of each angle relationship.
Vertical Angles Linear Pairs
Complementary Angles
Supplementary Angles
Angles that share a vertex and are formed by two pairs of opposite rays.*All vertical angles are congruent*
Two angles that share an adjacent side and whose other side is formed by an opposite ray.*The sum of a linear pair is *
Two angles whose sum is . Two angles whose sum is
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Try Some
Examples
Determine if the following angles are vertical, complementary, or supplementary.
ANGLE RELATIONSHIPS EXAMPLES
Show Answer
complementary
Show Answer
vertical
Show Answer
supplementary
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More Example
s
Refer to the figure to answer the following questions.
ANGLE RELATIONSHIP EXAMPLES
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More Example
s
Show Answer
and and
Show Answer
𝑚∠2=43 °
Show Answer
𝑚∠3=143 °
Use the diagram to answer the questions.
ANGLE RELATIONSHIP EXAMPLES
Show Answer ∠𝐶𝐵𝐷=31 °
Show Answer
or
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More Example
s
ANGLE RELATIONSHIP EXAMPLES
Use the diagram to answer the questions.
Show Answer ∠𝐶𝐵𝐷=61 °
Show Answer 𝑥=
803𝑜𝑟 26.66
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More Example
s
Use the diagram shown to answer the question.
ANGLE RELATIONSHIPS
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Show Answer
. If then so is not perpendicular to
TRIANGLES
The Triangle Sum Theorem:
For any triangle, the sum of all interior angles is .
.
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TRIANGLES
The Exterior Angle Theorem:For any triangle, an exterior angle is equal to the sum of the non-adjacent interior angles.
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CLASSIFYING TRIANGLES
By Sides:
Equilateral: 3 congruent sides
Isosceles: 2 congruent sides
Scalene: No congruent sides
By Angles:
Acute triangle: contains 3 acute angles
Equiangular triangle: contains 3 congruent angles (must be .
Right triangle: contains one right angle
Obtuse triangle: contains one obtuse angle
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Try Some
Examples
Use the diagram to answer the questions.
TRIANGLE EXAMPLES
Show Answer 𝑚∠2=36 °
Show Answer
Show Answer Return
to Main
More Example
s
ISOSCELES AND EQUILATERAL TRIANGLES
Equilateral:
3 congruent sides3 congruent angles ()
Isosceles:
2 congruent sides (legs) (non-congruent side is the base)2 congruent angles (base angles) (non-congruent angle is the vertex)
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Examples
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