Name_________________________________________ Date____________________ Class___________________
LESSON
Interior and Exterior Angles
7-1
Practice and Problem Solving: A/B
Find the measure of each angle.
1. 2.
mB ______ mF ______
4.
3.
mG ______ mL ______
5. 6.
mP ______ mVWY ______
Use your knowledge of angle relationships to answer questions 7–12.
7. The sum of the angle measures of a quadrilateral is ______.
8. The acute angles of a ____________ triangle are complementary.
9. The measure of an ____________ angle of a triangle is equal to the sum
of the measures of its remote interior angles.
10. The angle measures of a triangle are a, 3a, and 5a. Tell the measure
of each angle. ______, ______, ______
Name_________________________________________ Date____________________ Class___________________
11. You know that one of the exterior angles of an isosceles triangle is
140. The angle measures of the triangle could be ______-______-
______ or ______-______-______.
LESSON
Isosceles and Equilateral Triangles
7-2
Practice and Problem Solving: A/B
For Problems 1–6, find each value.
1. 2. 3.
mD ______ GI ______ mL ______
4. 5. 6.
RQ ______ mU ______ t ______
Use principles of isosceles and equilateral triangles to answer Problems 7–9.
7. Point M lies on side JL of triangle JKL. bisects and forms
equilateral triangle KLM. What is the measure of J? ________________
Make a sketch and explain your answer. ______________________________
______________________________________________________________________
______________________________________________________________________
8. Circle B and circle C are congruent. Point A is an
intersection of the two circles. Write a paragraph
proof to show that ∆ ABC is equilateral.
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
9. The Washington Monument is an obelisk, a tall, thin, four-sided
monument that tapers to a pyramidal top. Each face of the pyramidal
top of the Washington Monument is an isosceles triangle. The height
of each triangle is 55.5 feet, and the base of each triangle measures
Name_________________________________________ Date____________________ Class___________________
34.4 feet. Find the length, to the nearest tenth of a foot, of one of the
two congruent legs of the triangle. ___________________________
LESSON
Triangle Inequalities
7-3
Practice and Problem Solving: A/B
For Problems 1–3, name the angles or sides.
1. Write the angles of ∆≝¿ in order from smallest to largest.
_________ _________ _________
2. Write the sides of ∆ GHI in order from shortest to longest.
_________ _________ _________
3. The sides of triangle XYZ are given in order below from longest to
shortest. Name the angles from largest to smallest.
_________ _________ _________
Use your knowledge of triangle inequalities to solve Problems 4–7.
4. Can three segments with lengths 8, 15, and 6 make a triangle? Explain
your answer. ________________________________________________________
_____________________________________________________________________
5. For an isosceles triangle with congruent sides of length s, what is the
range of lengths for the base, b? What is the range of angle measures,
A, for the angle opposite the base? Write the inequalities and explain
your answers. _______________________________________________________
_____________________________________________________________________
6. Aaron, Brandon, and Clara sit in class so that they are at the vertices
of a triangle. It is 15 feet from Aaron to Brandon, and it is 8 feet from
Brandon to Clara. Give the range of possible distances, d, from Aaron
to Clara. ____________________________________________________________
7. Renaldo plans to leave from Atlanta and fly into London (4281 miles).
On the return, he will fly back from London to New York City (3470
miles) to visit his aunt. Then Renaldo heads back to Atlanta. Atlanta,
New York City, and London do not lie on the same line. Find the range
of the total distance Renaldo could travel on his trip. __________________
Name_________________________________________ Date____________________ Class___________________
MODULE 7 Properties of Their sum is 60, so each one is 30.
Triangles 8. It is given that circles B and C are
congruent. is a radius of circle B,
LESSON 7-1
is a radius of circle C, and is a radius
Practice and Problem Solving: A/B of both circles. All three segments are
1. 115 congruent because the radii of congruent
2. 70 circles are congruent. Therefore
is equilateral by definition because all
3. 60
three of its sides are congruent.
4. 65
9. 58.1 ft
5. 35
6. 120
LESSON 7-3
7. 360 Practice and Problem Solving: A/B
8. right 1. F; D; E
9. exterior
2.
10. 20, 60, 100
3. Y; X; Z
11. 40, 40, 100 or 40, 70, 70
4. The three segments cannot make a
triangle because 8 6 15; the two
shorter sides together do not reach from
LESSON 7-2
one end of the longer side to the other.
Practice and Problem Solving: A/B 5. 0 b 2s; 0 A 180
1. 50 If the congruent sides are very close
together, the base length is close to 0,
2. 6.3 and the measure of the angle opposite
3. 60 the base is close to 0. If the congruent
sides are very spread out, the base is
close to 2s (the combined length of the
4. 4 yd congruent sides), and the angle is close
5. 65 to 180.
6. 8 6. between 7 and 23 feet
7. 7. Renaldo could travel between 8562 miles
and 15,502 miles.
30. and are congruent
because they are the sides of an
equilateral triangle. is also congruent
to those three sides because M is the
midpoint of Angle KML is 60
because it is in an equilateral triangle.
Angles J and MKJ have the same
measure because they are opposite
congruent sides in an isosceles triangle.
