Download Honors Geometry Unit 1 Exam Review Review your Homework

Honors Geometry Unit 1 Exam Review
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Review your Homework Quizzes, Exit Slips and Embedded Assessments, then study homework
problems as needed.
Know your vocabulary and how is applies to problems like 20 & 26 on page 50.
Know how to write the converse & inverse of a conditional and determine validity.
Know how to write a two-column proof.
Know how to calculate and apply slope, distance, midpoint.
Be able to find the equation of a line that is perpendicular or parallel to another given line.
Understand and use the theorems and postulates we used with parallel lines and transversals.
Learning Targets
1-1-1
1-1-2
1-2-1
1-2-2
2-1-1
2-2-1
2-2-2
3-1-2
3-2-1
3-2-2
3-3-1
3-3-2
4-1-1
4-1-2
4-2-1
4-2-2
5-1-2
5-2-2
6-1-1
6-1-2
6-2-1
6-2-2
7-1-1
7-1-2*
7-2-2
8-1-1*
8-1-2
8-2-1
8-2-2
Identify, describe, and name points, lines, line segments, rays and planes using correct notation.
Identify and name angles.
Describe angles and angle pairs.
Identify and name parts of a circle.
Make conjectures by applying inductive reasoning.
Use deductive reasoning to prove that a conjecture is true.
Develop geometric and algebraic arguments based on deductive reasoning.
Use properties to complete algebraic two-column proofs.
Identify the hypothesis and conclusion of a conditional statement.
Give counterexamples for false conditional statements.
Write and determine the truth value of the converse, inverse, and contrapositive of a conditional statement.
Write and interpret biconditional statements.
Apply the Segment Addition Postulate to find lengths of segments.
Use the definition of midpoint to find lengths of segments.
Apply the Angle Addition Postulate to find angle measures.
Use the definition of angle bisector to find angle measures.
Use the Distance Formula to find the distance between two points on the coordinate plane.
Use the Midpoint Formula to find the coordinates of the midpoint of a segment on the coordinate plane.
Use definitions, properties, and theorems to justify a statement.
Write two-column proofs to prove theorems about lines and angles.
Complete two-column proofs to prove theorems about segments.
Complete two-column proofs to prove theorems about angles.
Make conjectures about the angles formed by a pair of parallel lines and a transversal.
Prove theorems about the angles formed by a pair of parallel lines and a transversal..
Determine whether lines are parallel using theorems.
Make conjectures about the slopes of parallel and perpendicular lines.
Use slope to determine whether lines are parallel or perpendicular.
Write the equation of a line that is parallel to a given line.
Write the equation of a line that is perpendicular to a given line.
Vocab to Know
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
angle
adjacent angles
acute angle
axiomatic system
bi-conditional statement
bisector (angle & segment)
alternate interior angles
chord
complementary angles
congruent
coplanar, collinear
conditional statement (hypothesis and
conclusion)
conjecture
concentric
contrapositive
converse
corresponding angles
counterexample
diameter
deductive reasoning
inductive reasoning
inverse
line
linear pair
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
35.
36.
37.
38.
39.
40.
41.
42.
43.
44.
45.
46.
47.
48.
49.
midpoint
obtuse angle
straight angle
parallel lines
perpendicular lines
same-side interior angles
supplementary angles
plane
point
postulate
proof
theorem
transversal
truth value
two-column proof
radius
ray
right angle
segment
undefined terms
vertical angles
segment or angle addition postulate
Vertical angles theorem
Alternate exterior angles
Same side exterior angles
Not every type of problem on the exam is represented below, however these problems will allow you
to refresh your memory on some concepts that you will see on the exam. It is in your best interest to
use your class notes, textbook examples and homework problems to be fully prepared for the exam.
1) Complete a two-column proof:
⃗⃗⃗⃗⃗ bisects EPG
Given: 𝑷𝑭
Prove: EPF = 26 o
2) Write each of the following in if-then form. Write the converse of each statement and discuss the
validity of each converse.
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Rectangles have four sides
Three points on the same line are collinear
3) Write the equation of a line parallel to the given line and through the given point.
𝑦=
1
𝑥 + 3,
2
(6,3)
4) 𝑎 ∥ 𝑏. Find x. Explain your reasoning.
5) Name the angle or angles described by each of the following:
a) supplementary to NQK
b) vertical to PQM
c) congruent to NQJ
d) adjacent and congruent to JQM
e) complimentary to KQP
e) forms a linear pair with PQM
6) A map of a city and suburbs shows an airport located at A(25, 11). An ambulance is on a straight
expressway headed from the airport to Grant Hospital at G(1, 1).
a. The ambulance gets a flat tire at the midpoint M of AG . What are their coordinates?
b. How far are they from the hospital?
c. Write the equation of a line that is perpendicular to AG going through the point (6,7).
7) Write a two-column proof.
Given: a b , c d
Prove: ∢𝟏𝟔 ≅ ∢𝟐
8) Point E is between G and T, GE  2 x, ET  (3x  1) and GT  14 Find the value of x.
Geometry Unit 1 Review Answers
Statements
⃗⃗⃗⃗⃗
𝑃𝐹 bisects ∡𝐸𝑃𝐺
∢𝐸𝑃𝐹 ≅ ∢𝐹𝐷𝐺
4x+2=6x-10
2=2x-10
12=2x
X=6
∢𝐸𝑃𝐹 = 4(6) + 2
∢𝐸𝑃𝐹 = 26
Reasons
Given
Definition of bisects
Substitution property
Subtraction property of equality
Addition property of equality
Division property of equality
Substitution property
Substitution Property
1.) Conditional – If a figure is a rectangle, then it has 4 sides.
Converse – If a figure has 4 sides, then it is a rectangle.
The converse is false. Counterexample – Parallelogram.
Conditional – If 3 points lie on the same line, then they are collinear.
Converse – If 3 points are collinear, then they are on the same lie.
The converse if true by the definition of collinear.
1
2
2.) 𝑦 = 𝑥
3.) X=54, the angles are congruent by the alternate exterior angles theorem. OR Students could
use corresponding angles and vertical angles to explain why the angles are congruent.
4.) Sample Answers
A. ∢𝑁𝐽𝑄 𝑜𝑟 ∡𝐾𝑄𝑃
B. ∢𝐿𝑄𝑁
C. ∢𝐾𝑄𝑃
D. ∢𝐾𝑄𝑀 𝑜𝑟 ∢𝐿𝑄𝐽
E. ∢𝑃𝑄𝑀
F. ∢𝑀𝑄𝑁 𝑜𝑟 ∢𝐿𝑄𝑃
6.) M (13,6) and d=13 units
7.) Sample Answer
Statements
8.) x=3
Reasons
a b, c d
given
∠16 ≅ ∠10
Corresponding angles postulate
∠10 ≅ ∠2
Alternate Interior angles theorem
∠16 ≅ ∠2
Transitive property