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Geometry SOL G.2, G.5 STUDY GUIDE
Inequalities
Parallel/Perpendicular Lines, Triangle
Name: ________________________________________ Date: _______________ Block: _________
Geometry Parallel/Perpendicular Lines, Triangles Intro STUDY GUIDE
SOLs: G.2, G.5
Things to Know:

Quizlet flashcards can be found here: http://quizlet.com/7099704/geometry-chapter3-parallel-perpendicular-lines-flash-cards/

Identify corresponding, alternate interior, alternate exterior, corresponding interior, and
vertical angles formed when a transversal crosses two lines (parallel or not).

Know congruence/supplementary postulate/theorems for these angles if the transversal
crosses parallel lines; find missing angle values based on these theorems.

Apply the converse theorems of above: be able to find missing angle values that would
make lines parallel.

Be able to identify whether lines are parallel or perpendicular, given the lines themselves
or two points on a line.

Be able to graph parallel or perpendicular lines through a point relative to a given line.

Be able to write a linear equation that is parallel or perpendicular to a given line that
passes through a point not on the line.

Be able to find the distance, using the distance formula, between two parallel lines.

Be able to classify a triangle by its sides (scalene, isosceles, equilateral) or its angles
(acute, right, obtuse, equiangular).

Find missing angle measures in a triangle by applying the triangle sum theorem and its
corollary. Be able to apply the exterior angle theorem as well.

Use the fact that corresponding parts of congruent angles are congruent to find angle or
side measures of congruent triangles.

Be able to determine whether three given side lengths could form a triangle.

Given two side lengths of a triangle, be able to find the possible lengths of the third side.

Given the angle measures of a triangle, be able to list the sides in order from least to
greatest or greatest to least. Be able to list the angles in size order given the side
lengths.

Apply the Hinge Theorem to determine whether sides or angles or less than, equal to, or
greater than sides or angles in another triangle, or to find restrictions on side lengths.
Practice questions:
1) Classify the angle pair as corresponding, alternate interior,
alternate exterior, consecutive interior, or vertical angles:
a) 6 and 2
b) 7 and 2
c) 5 and 3
Geometry SOL G.2, G.5 STUDY GUIDE
d) 4 and 5
Parallel/Perpendicular Lines, Triangle Inequalities Page 2
e) 1 and 5
f) 5 and 8
2) Find the value of x.
a)
b)
3) Find the value of x and y.
a)
b)
4) Find the value of x that makes m || n . State the theorem or postulate you used.
a)
b)
Theorem/Postulate: _____________________
Theorem/Postulate: _______________________
5) Tell whether the lines through the given points are parallel, perpendicular, or neither.
a) Line 1: (7, 4), (10, 5); Line 2: (2, 3), (8, 5)
b) Line 1: (-6, 0), (8, 7); Line 2: (1, 4), (2, 2)
c) Line 1: (-3, 1), (-2, 5); Line 2: (-1, -3), (5, -2)
6) Write an equation of the line that passes through point P and is parallel to the given
line:
a) P(1, -2); y = -2x + 6
b) P(-7, 3); y = x + 3
7) Write an equation of the line that passes through point P and is perpendicular to the
given line:
Geometry SOL G.2, G.5 STUDY GUIDE
Parallel/Perpendicular Lines, Triangle Inequalities Page 3
a) P(3, -1); y = 6x – 4
b) P(-1, 1); 3y – 7x = 30
8)
a) Write an equation of the line shown:
b) Graph the equation: 2x + 4y = 3
9) Graph the line that passes through point P that is parallel or perpendicular to the given
line; what are the slopes of the lines?
a) Parallel to AB ; P(-1, 2)
b) Perpendicular to AB ; P(-1, 3)
10) Find the mADB :
a)
b)
11) Use the distance formula to find the distance between the line
and point (put answer in simplest radical form, then round to the
nearest tenth):
12) Classify the triangle by its sides and angles.
Geometry SOL G.2, G.5 STUDY GUIDE
a)
Parallel/Perpendicular Lines, Triangle Inequalities Page 4
b)
c)
d)
13) Find the value of x, and find the missing angle measures. Then classify the triangle by
its angles.
a)
b)
c)
d)
14) Find the value of x.
a)
b)
15) Is it possible to construct a triangle with the given side lengths? If not, why not?
a) 6, 10, 15
b) 11, 16, 32
c) 7, 54, 45
16) Given the two sides of a triangle, describe the possible lengths of x, the third side.
a) 4 ft and 10 ft
b) 11 m and 10 m
c) 7 in and 1 ft
17) Given the angles of a triangle, list the sides in order from smallest to largest.
a)
b)
c)
Geometry SOL G.2, G.5 STUDY GUIDE
Parallel/Perpendicular Lines, Triangle Inequalities Page 5
18) Given the sides of a triangle, list the angles in order from smallest to largest.
a)
b)
c)
19) In KLM , mL  mK  mM . List the sides in order from smallest to largest.
20) In XYZ , XZ = 32, XY = 20, and YZ = 29. Order the angles of the triangle in order from
smallest to largest.
21) Find the value of x and the angle measures using the triangle sum theorem; then list
the sides of ABC in order from shortest to longest:
mA  (9 x  29); mB  (93  5x), and mC  (10 x  2)
22) A triangle has sides that are about 33, 18, and 24 cm long, and angles of 32 , 103 , and
45 . Sketch and label a diagram with these angle measures and side lengths.
23) Complete the statement with >, <, or =.
a) JL ________ ST
b) mDEG ________ mFEG
c) m1 ________ m2
d) AB ________ CD
e) m1 ________ m2
f) AT ________ BT
24) Use the diagram to find the inequality that describes the
restriction on the value of x.
Geometry SOL G.2, G.5 STUDY GUIDE
Parallel/Perpendicular Lines, Triangle Inequalities Page 6
Study Guide Answers
1)
2)
3)
4)
a) corresponding b) alt. exterior c) consec. interior d) alt. interior e) corresponding f) vertical
a) x=43 b) x=31
a) x=9, y = 1 b) x=30, y=10
a) x=107(if two consecutive interior angles are supplementary, then the lines are ||)
b) x=133 (if two alternate exterior angles are  , then the lines are ||)
5) a) parallel b) perpendicular c) neither
6) a) y  2 x b) y  x  10
1
1
3
4
b) y   x 
6
2
7
7
8) a) y  2 x  1 b)
7) a) y   x 
9) a) both
lines
have
m=1
b)original line m  
4
;
3
perpendicular line through P:
m
3
4
10) a) 52 b) 59
11) 8  2 2  2.8
12) a) scalene; obtuse b) equilateral; equiangular/acute c) isosceles; right d) isosceles; obtuse
13) a) x=12; mA  47 , mB  90 , mC  43 ; right
b) x=26; mB  52 , mBCA  52 , mBCD  128 ; acute
c) x=30; mBDC  60 , mCBD  90 , mABD  90 ; right
d) x=10; mCAB  80 , mABC  10 , mACB  90 ; right
14) a) x=65 b) x=2
15) a) yes (sum of 2 sides always bigger than 3rd) b) no; 11+16<32 c) no; 7+45<54
16) a) 6 ft  x  14 ft b) 1 m  x  21 m c) convert to inches: 5 in  x  19 in
17) a) AB < AC < BC b) BC < AB < AC c) GI < GH < HI
18) a) mE  mD  mF b) mE  mF  mD c) mJ  mL  mK
19) KM < LM < KL
20) mZ  mX  mY
21) x=4; mA  65; mB  73; mC  42 ; AB < BC < AC
22)
23) a) < b) > c) = d) < e) > f) >
24) x  4