Transcript Slide 1 - baumherclasses

Geometry/Trig 2
Name: __________________________
Unit 3 Review Packet ANSWERS
Date: ___________________________
Section I – Name the five ways to prove that parallel lines exist.
1. If two lines are cut by a transversal and the corresponding angles are congruent, then the lines
are parallel. (Show 1 pair of corresponding angles are congruent.)
2. If two lines are cut by a transversal and the alternate interior angles are congruent, then the
lines are parallel. (Show 1 pair of alternate interior angles are congruent.)
3. If two lines are cut by a transversal and the same side interior angles are supplementary, then
the lines are parallel. (Show 1 pair of same side interior angles totals 180)
4. If 2 lines are parallel to the same line, then they are parallel to each other. (Show that both lines
are parallel to a third line.)
5. If 2 lines are perpendicular to the same line they are parallel to each other. (Show that both
lines are perpendicular to a third line)
Section II – Identify the pairs of angles.
1. 1 & 4 ___Vertical angles_____
1
2. 3 & 6 ___Alternate Interior Angles_
3
2
4
3. 8 & 4 ___Corresponding Angles__
4. 2 & 7 ___Alternate Exterior Angles
5. 3 & 5 __Same Side Interior Angles_
6
5
7
8
6. 1 & 6 ___none______________
Section III – Fill In
1.) Vertical angles p are ____congruent____
2.) Angles in a linear air are ____Supplementary___________.
3.) If two parallel lines are cut by a transversal, then corresponding angles are ____congruent______.
4.) If two parallel lines are cut by a transversal, then alternate interior angles are ___congruent_____.
5.) If two parallel lines are cut by a transversal, then alternate exterior angles are ___congruent___.
6.) If two parallel lines are cut by a transversal, then same side interior angles are __Supplementary__.
7.) If two parallel lines are cut by a transversal, then same side exterior angles are ___Supplementary_.
8. If two lines are perpendicular to a third, then the two lines are __parallel_________________.
9. The sum of interior angles of a ____triangle___ is 180.
10. The measure of an exterior
of a triangle is the sum of the two _non-adjacent_ _interior_ _angles.
Geometry/Trig 2
Name: __________________________
Unit 3 Review Packet – Page 2
Date: ___________________________
Section IV – Determine which lines, if any, are parallel based on the given information. If
there are parallel lines, state the reason they are parallel.
1.) m1 = m9
___c//d______If Corresponding
1 2
3 4
a
s are  the lines are //____
2.) m1 = m4
___none, because the angles are b
5 6
7 8
9 10
11 12
13 14
15 16
vertical.
3.) m12 + m14 = 180
a//b, If Same side interior s
are supplementary the lines are //
4.) m1 = m13
_none, angles do not share the
same transversal____
5.) m7 = m14
c//d; 1415, vertical  s are 
715 , If Corresponding s are
 the lines are //
6.) m2 = m11
c//d, If alternate interior
s are , the lines are //
7.) m15 + m16 = 180
_none, linear pair__________
_________________________
8.) m4 = m5
a//b, If alternate interior
s are , the lines are //
c
d
Geometry/Trig 2
Name: __________________________
Unit 3 Review Packet – Page 3
Date: ___________________________
Section V – Name the following polygons – For triangles name each by side and angles; for all
other polygons name whether each is irregular or regular, convex or not convex, and give its
name based on the number of sides.
1.
2.
Pentagon, convex,
regular
Triangle, scalene
right
5
3
4
3.
4.
60
Pentagon, concave,
irregular
60
5.
Triangle, isosceles,
obtuse
Triangle, acute
equilateral,
(equiangular)
60
6.
Quadrilateral,
regular, convex
8
5
5
7.
9
7
8
Triangle, scalene
acute
square
8.
Heptagon, concave,
irregular
Section VI – Fill In the Chart
Number of
Sides
Name of
polygon
Sum of
interior
angles.
Measure of each
interior angle if it
was a regular polygon
Sum of
exterior
angles.
4
Quadrilateral
360°
90°
360°
8
Octagon
1080°
135°
360°
10
Decagon
1440°
144°
360°
3
Triangle
180°
60°
360°
5
Pentagon
540°
108°
360°
7
Heptagon
900°
128.5°
360°
6
Hexagon
720°
120°
360°
Section VII– Find the slope of each line. (Change the equations into slope intercept
form.) Determine which lines are parallel and which lines are perpendicular.
Line a 8x – 2y = 10
y=4x-5, m=4
Line b 4y = 6x
Line c 2x - 3y = 9
y=-2/3x-3, m=-2/3
Line d y = x
Line e x + y = 2
y=-x+2, m=-1
Line f 5x – 4y = 4 y=5/4x-1, m=5/4
Parallel lines _____d//e__________
Perpendicular lines ___bc______
________________
y=3/2x, m=3/2
m=1
Geometry/Trig 2
Name: __________________________
Unit 3 Review Packet – Page 4
Date: ___________________________
Section X - Proofs
Given: GK bisects JGI
J
mH = m2
Statements
Reasons
1. GK bisects JGI
1. Given
2. 1  2
2.
Defn of  bisector
3.
Given
4. 1  H
4.
Substitution prop of =
5. GK // HI
5.
3. H  2
1
2
G
Prove: GK // HI
K
I
H
If corresponding s are , then the
lines are //
Given: AJ // CK; m1 = m5
Statements
Reasons
Prove: BD // FE
1. AJ // CK
1. Given
2. 1  4
2. If 2 lines are //, then alt int
s are 
3. 1  5
3. Given
4. 4  5
5. BD // EF
A
4. Substitution pro of =
5. If alt int s are , then the
B
lines are //
F
C
1
2
4
5
J
K
3
D
E