FREE NJGPA Applying Geometric Theorems Questions and Answers

Question 1

A 15-foot ladder is leaning against a wall. The base of the ladder is 9 feet away from the base of the wall. How high up the wall does the ladder reach?

Accepted Answer

12 feet

Answer

This scenario forms a right triangle, with the ladder as the hypotenuse. Using the Pythagorean theorem (a² + b² = c²), we have a² + 9² = 15². This simplifies to a² + 81 = 225. Subtracting 81 gives a² = 144. Taking the square root, a = 12 feet.

Question 2

A triangle has side lengths of 8 cm, 15 cm, and 17 cm. Which statement is true about this triangle?

Accepted Answer

It is a right triangle.

Answer

To determine if it's a right triangle, use the converse of the Pythagorean theorem: a² + b² = c². Check if 8² + 15² = 17². This becomes 64 + 225 = 289, which simplifies to 289 = 289. Since the equation is true, the triangle is a right triangle.

Question 3

In two triangles, two pairs of corresponding angles and the pair of corresponding non-included sides are congruent. Which theorem proves the triangles are congruent?

Accepted Answer

Angle-Angle-Side (AAS)

Answer

The Angle-Angle-Side (AAS) congruence theorem states that if two angles and a non-included side of one triangle are congruent to the corresponding two angles and non-included side of another triangle, then the triangles are congruent. The description matches this theorem perfectly.

Question 4

Given that ΔABC ≅ ΔXYZ, AB = 2x + 1, and XY = 15. What is the value of x?

Accepted Answer

x = 7

Answer

If two triangles are congruent, their corresponding parts are congruent (CPCTC). Therefore, side AB corresponds to side XY, and their lengths must be equal. Set up the equation 2x + 1 = 15. Solving for x gives 2x = 14, so x = 7.

Question 5

A 6-foot tall person casts a 4-foot shadow. At the same time, a nearby flagpole casts a 20-foot shadow. How tall is the flagpole?

Accepted Answer

30 feet

Answer

The person and their shadow, and the flagpole and its shadow, form two similar right triangles. Set up a proportion of corresponding sides: (person's height) / (person's shadow) = (flagpole's height) / (flagpole's shadow). This gives 6/4 = h/20. Cross-multiply to get 4h = 120, so h = 30 feet.

(NJGPA) New Jersey Graduation Proficiency Assessment Practice Test

(NJGPA) New Jersey Graduation Proficiency Assessment Practice Test

FREE NJGPA Applying Geometric Theorems Questions and Answers