NJGPA Applying Geometric Theorems 3

Question 1

A tangent and a secant are drawn from an external point to a circle. The tangent has length 8 and the external segment of the secant is 4. What is the length of the whole secant?

Accepted Answer

16

Answer

Tangent-secant theorem: tangent² = external segment × whole secant, so 64 = 4 × whole secant, giving 16.

Question 2

In a regular hexagon, what is the measure of each interior angle?

Accepted Answer

120°

Answer

Each interior angle of a regular hexagon = (6 − 2) × 180° ÷ 6 = 720° ÷ 6 = 120°.

Question 3

Line segment MN has midpoint P. If M is at (2, 4) and P is at (5, 7), what are the coordinates of N?

Accepted Answer

(8, 10)

Answer

Using the midpoint formula in reverse: N = (2×5 − 2, 2×7 − 4) = (8, 10).

Question 4

In triangle XYZ, XY is parallel to a line segment connecting the midpoints of XZ and YZ. If XY = 14, what is the length of the midsegment?

Accepted Answer

7

Answer

By the Triangle Midsegment Theorem, the midsegment is half the length of the parallel side: 14 ÷ 2 = 7.

Question 5

Angles A and B are vertical angles. If angle A = (3x + 10)° and angle B = (5x − 6)°, what is x?

Accepted Answer

8

Answer

Vertical angles are congruent: 3x + 10 = 5x − 6, so 16 = 2x, giving x = 8.

(NJGPA) New Jersey Graduation Proficiency Assessment Practice Test

(NJGPA) New Jersey Graduation Proficiency Assessment Practice Test

NJGPA Applying Geometric Theorems 3