Geometry — Semester A
Free Practice · 12 Questions
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Question 1 of 12
TEKS 1A-1G Easy
A ladder leans against a wall, reaching a window 12 feet above the ground. The base of the ladder is 5 feet from the wall. How long is the ladder?
A 11 feet
B 12 feet
C 13 feet
D 17 feet
Explanation

Use the Pythagorean theorem: a² + b² = c². So 12² + 5² = 144 + 25 = 169. √169 = 13 feet.

Question 2 of 12
TEKS 1A-1G Easy
A triangular park has sides of 7 km, 24 km, and 25 km. Is this a right triangle?
A Yes, because 7 + 24 = 31 > 25
B Yes, because 7² + 24² = 25²
C No, because 25 is too large
D No, because the sides are not equal
Explanation

7² + 24² = 49 + 576 = 625 = 25². Since a² + b² = c², it is a right triangle.

Question 3 of 12
TEKS 1A-1G Medium
A square has a diagonal of 10√2 cm. What is the side length of the square?
A 5 cm
B 10 cm
C 14.1 cm
D 20 cm
Explanation

For a square with side s, the diagonal = s√2. So s√2 = 10√2, meaning s = 10 cm.

Question 4 of 12
TEKS 2A-2C Easy
What is the distance between points A(2, 3) and B(6, 6)?
A 4
B 5
C 6
D 7
Explanation

d = √((6−2)² + (6−3)²) = √(16 + 9) = √25 = 5.

Question 5 of 12
TEKS 2A-2C Medium
Line ℓ has slope 3/4. What is the slope of a line perpendicular to ℓ?
A 4/3
B −3/4
C −4/3
D 3/4
Explanation

Perpendicular slopes are negative reciprocals. The negative reciprocal of 3/4 is −4/3.

Question 6 of 12
TEKS 4A-4D Easy
Given the conditional statement "If it rains, then the ground is wet," what is the contrapositive?
A If the ground is wet, then it rains
B If it does not rain, then the ground is not wet
C If the ground is not wet, then it does not rain
D If the ground is wet, then it does not rain
Explanation

The contrapositive reverses and negates both parts: "If the ground is not wet, then it does not rain." A contrapositive always has the same truth value as the original.

Question 7 of 12
TEKS 5A-5D Easy
Two parallel lines are cut by a transversal. One of the alternate interior angles measures 65°. What is the measure of the other alternate interior angle?
A 25°
B 65°
C 115°
D 180°
Explanation

Alternate interior angles are congruent when formed by parallel lines and a transversal. So the other angle is also 65°.

Question 8 of 12
TEKS 6A-6E Easy
Two vertical angles are formed by intersecting lines. If one angle measures 48°, what is the measure of the other vertical angle?
A 42°
B 48°
C 132°
D 90°
Explanation

Vertical angles are always congruent. The other angle is also 48°.

Question 9 of 12
TEKS 7A-7B Easy
A triangle with sides 3, 4, and 5 is dilated by a scale factor of 3. What are the side lengths of the new triangle?
A 6, 7, 8
B 6, 8, 10
C 9, 12, 15
D 12, 16, 20
Explanation

Multiply each side by the scale factor: 3×3=9, 4×3=12, 5×3=15.

Question 10 of 12
TEKS 8A-8B Medium
In △ABC, line DE is parallel to BC with D on AB and E on AC. If AD = 6, DB = 4, and AE = 9, what is EC?
A 4
B 6
C 8
D 10
Explanation

By the Triangle Proportionality Theorem: AD/DB = AE/EC → 6/4 = 9/EC → EC = 9 × 4/6 = 6.

Question 11 of 12
TEKS 9A-9B Easy
In a 45-45-90 triangle, if one leg is 8, what is the length of the hypotenuse?
A 8
B 8√2
C 16
D 8√3
Explanation

In a 45-45-90 triangle, hypotenuse = leg × √2. So 8√2 ≈ 11.31.

Question 12 of 12
TEKS 6A-6E Easy
In the triangle below, ∠A = 55° and ∠B = 65°. What is the measure of ∠C? A B C 55° 65° ?
A 50°
B 60°
C 70°
D 75°
Explanation

The sum of angles in a triangle is 180°. ∠C = 180° − 55° − 65° = 60°.

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