Name _______________________________________ Date __________________ Class __________________
LESSON
15-3
Relationships Between Sides and Angles in a Triangle
Practice and Problem Solving: A/B
Use the triangles shown below to complete Exercises 1–6.
1.
2.
w  ____________
3.
y  ____________
r  ____________
4. The longest side in the triangle in Exercise 1 is opposite the ______ angle.
5. How do the lengths of the sides compare in the triangle in Exercise 2?
________________________________________________________________________________________
6. The shortest side in the triangle in Exercise 3 is opposite the ______ angle(s).
Solve. Show your work.
7. The shortest side of triangle ABC is half of the second side and a third
of the longest side. How does the perimeter of the triangle compare to
the longest side?
________________________________________________________________________________________
________________________________________________________________________________________
8. In triangle DEF, side DE is 3 inches, side EF is 4 inches, and side DF
is 5 inches. The largest angle is opposite which side? Explain your
choice.
________________________________________________________________________________________
9. Angle X is the largest angle in triangle XYZ. Angle Y is the smallest
angle. How does the sum of the measures of angles Y and Z compare
to the measure of angle X? Explain.
________________________________________________________________________________________
Describe each statement as always, never, or sometimes true.
10. An obtuse triangle is a scalene triangle. _________________________________________
11. A scalene triangle is an isosceles triangle. _______________________________________
12. A right triangle is an isosceles triangle. __________________________________________
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
309
Name _______________________________________ Date __________________ Class __________________
LESSON 15-3
Practice and Problem Solving: A/B
1. 68
2. 60
3. 62
4. 68
5. They are equal.
6. 56
7. shortest: x, second: 2x, third: 3x;
P  x  2x  3x  6x; longest side  3x
The longest side is one half of the
perimeter.
8. Side DF, since it is the longest side.
9. The sum of the measures of angles Y
and Z is less than twice the measure
of angle X.
10. Sometimes, e.g. a triangle with angles
of 155, 20, and 5.
11. Never, since an isosceles triangle has
two equal sides and all of the sides in a
scalene triangle are unequal.
12. Sometimes, e.g. a 454590 right
triangle is the only isosceles right
triangle.
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
309