AnswersPARTA - EOP PGCPS GEOMETRY OC FALL2026 - 793413Congruent and Similar Triangles in the Coordinate Plane

Triangle Classification Theorems Answers

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Which set of numbers can represent the side lengths, in inches, of an acute triangle?

A
4, 5, 7
B
5, 7, 8
C
6, 7, 10
D
7, 9, 12
2
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The shorter sides of an acute triangle are x cm and 2x cm. The longest side of the triangle is 15 cm.What is the smallest possible whole-number value of x?

A
6
B
7
C
8
D
9
3

A right triangle has side lengths 4 units, 5 units, and x units. It is unknown if the missing length is the longest or shortest side.Rounded to the nearest tenth, what is the difference between the possible values of x?

A
3.0 units
B
3.4 units
C
6.4 units
D
8.0 units
4

The longest side of an acute isosceles triangle is 12 centimeters. Rounded to the nearest tenth, what is the smallest possible length of one of the two congruent sides?

A
6.0 cm
B
6.1 cm
C
8.4 cm
D
8.5 cm
5

Which best explains whether a triangle with side lengths 5 cm, 13 cm, and 12 cm is a right triangle?

A
The triangle is a right triangle because 52 + 122 = 132.
B
The triangle is a right triangle because 5 + 13 > 12.
C
The triangle is not a right triangle because 52 + 132 > 122.
D
The triangle is not a right triangle because 5 + 12 > 13.
6

Two sides of an obtuse triangle measure 12 inches and 14 inches. The longest side measures 14 inches.What is the greatest possible whole-number length of the unknown side?

A
2 inches
B
3 inches
C
7 inches
D
9 inches
7

The longest side of an acute triangle measures 30 inches. The two remaining sides are congruent, but their length is unknown.What is the smallest possible perimeter of the triangle, rounded to the nearest tenth?

A
41.0 in.
B
51.2 in.
C
72.4 in.
D
81.2 in.
8

Which set of numbers can represent the side lengths, in centimeters, of a right triangle?

A
8, 12, 15
B
10, 24, 26
C
12, 20, 25
D
15, 18, 20
9

Two sides of an acute triangle measure 5 inches and 8 inches. The length of the longest side is unknown.What is the greatest possible whole-number length of the unknown side?

A
8 inches
B
9 inches
C
12 inches
D
13 inches
10

Which classification best represents a triangle with side lengths 6 cm, 10 cm, and 12 cm?

A
acute, because 62 + 102 < 122
B
acute, because 6 + 10 > 12
C
obtuse, because 62 + 102 < 122
D
obtuse, because 6 + 10 > 12

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