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Glencoe/McGraw-Hill
8787 Orion Place
Columbus, Ohio 43240
Lesson 5-1 Bisectors, Medians, and Altitudes
Lesson 5-2 Inequalities and Triangles
Lesson 5-3 Indirect Proof
Lesson 5-4 The Triangle Inequality
Lesson 5-5 Inequalities Involving Two Triangles
Example 1 Compare Angle Measures
Example 2 Exterior Angles
Example 3 Side-Angle Relationships
Example 4 Angle-Side Relationships
Determine the relationship between the measures of
RSU and SUR.
Answer: The side opposite RSU is longer than the side
opposite SUR, so mRSU > mSUR.
Determine the relationship between the measures of
TSV and STV.
Answer: The side opposite TSV is shorter than the side
opposite STV, so mTSV < mSTV.
Determine the relationship between the measures of
RSV and RUV.
mRSU > mSUR
mUSV > mSUV
mRSU + mUSV > mSUR + mSUV
mRSV > mRUV
Answer: mRSV > mRUV
Determine the relationship between the measures of
the given angles.
a. ABD, DAB
Answer: ABD > DAB
b. AED, EAD
Answer: AED > EAD
c. EAB, EDB
Answer: EAB < EDB
HAIR ACCESSORIES Ebony is following directions
for folding a handkerchief to make a bandana for her
hair. After she folds the handkerchief in half, the
directions tell her to tie the two smaller angles of the
triangle under her hair. If she folds the handkerchief
with the dimensions shown, which two ends should
she tie?
Theorem 5.10 states that if one side of a triangle is longer
than another side, then the angle opposite the longer side
has a greater measure than the angle opposite the shorter
side. Since X is opposite the longest side it has the
greatest measure.
Answer: So, Ebony should tie the ends marked Y and Z.
KITE ASSEMBLY Tanya is following directions for
making a kite. She has two congruent triangular
pieces of fabric that need to be sewn together along
their longest side. The directions say to begin sewing
the two pieces of fabric together
at their smallest angles.
At which two angles
should she begin
sewing?
Answer: A and D
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