Geometry — Semester B Practice

Question 1 of 10

TEKS 3A-3D Hard Calc Word

Point Q(4, −1) is first reflected across the y-axis, then rotated 180° about the origin. What is the final image?

A (4, −1)

B (−4, −1)

C (4, 1)

D (−4, 1)

Explanation

📌 Step 1: Understand rigid motions (isometries)
Transformations that preserve BOTH size and shape:
✅ Translation (slide)
✅ Reflection (flip)
✅ Rotation (turn)

📌 Step 2: Non-rigid transformations
❌ Dilation — changes size
❌ Stretches/compressions — distort shape

📌 Answer: Translation preserves both size and shape.

💡 Key term: Rigid motions are also called "isometries" (iso = same, metry = measure).

Question 2 of 10

TEKS 12A-12E Medium Calc Word Diagram

A tangent line touches circle O at point T. OT = 5 and the external point P is 13 units from the center O. What is the length of tangent segment PT?

A 8

B 10

C 14

D 12

Explanation

The tangent is perpendicular to the radius at the point of tangency. Using the Pythagorean theorem: PT = √(OP² − OT²) = √(13² − 5²) = √(169 − 25) = √144 = 12.

Question 3 of 10

TEKS 1A-1G Easy Calc Word

A cylindrical water tank has a radius of 3 feet and a height of 8 feet. What is the volume of the tank? (Use π ≈ 3.14)

A 301.44 ft³

B 75.36 ft³

C 150.72 ft³

D 226.08 ft³

Explanation

📌 Step 1: Recall the volume formula for a cylinder
V = πr²h

📌 Step 2: Plug in the values
r = 3 ft, h = 8 ft, π ≈ 3.14
V = 3.14 × 3² × 8 = 3.14 × 9 × 8

📌 Step 3: Calculate
3.14 × 9 = 28.26
28.26 × 8 = 226.08 ft³

💡 Tip: Always check your units — volume is measured in cubic units (ft³, cm³, m³).

Question 4 of 10

TEKS 11A-11D Medium Calc Word Diagram

Find the volume of the cone shown below. Round to the nearest tenth. (Use π ≈ 3.14)

A 339.1 cm³

B 565.2 cm³

C 452.2 cm³

D 1695.6 cm³

Explanation

📌 Step 1: Recall the cone volume formula
V = (1/3)πr²h

📌 Step 2: Plug in values
r = 6 cm, h = 15 cm
V = (1/3)(3.14)(36)(15)

📌 Step 3: Calculate step by step
3.14 × 36 = 113.04
113.04 × 15 = 1695.6
1695.6 / 3 = 565.2 cm³

💡 Common mistake: Don't forget to divide by 3! A cone is 1/3 the volume of a cylinder with the same base and height.

Question 5 of 10

TEKS 3A-3D Easy Calc Word Diagram

Which of the following figures has BOTH reflectional and rotational symmetry?

A B (Regular hexagon)

B D (Arrow)

C C (Parallelogram)

D A (Scalene triangle)

Explanation

📌 Step 1: Check each figure

A (Scalene triangle): No lines of symmetry, no rotational symmetry ✗
B (Regular hexagon): 6 lines of symmetry + rotational symmetry at 60° ✓
C (Parallelogram): No lines of symmetry, rotational symmetry at 180° only → partial ✗
D (Arrow): 1 line of symmetry (vertical) but no rotational symmetry ✗

📌 Answer: B (Regular hexagon)

💡 Tip: All regular polygons have BOTH reflectional AND rotational symmetry. The number of symmetry lines = number of sides.

Question 6 of 10

TEKS 1A-1G Hard Calc Word

A composite figure is made of a rectangle (10 m × 6 m) with a semicircle attached to one of the shorter sides. What is the total area? (Use π ≈ 3.14)

A 64.7 m²

B 102.5 m²

C 88.3 m²

D 74.1 m²

Explanation

📌 Step 1: Break into simple shapes
Rectangle: 10 m × 6 m
Semicircle: radius = 6/2 = 3 m (attached to the 6 m side)

📌 Step 2: Calculate each area
Rectangle = 10 × 6 = 60 m²
Semicircle = ½πr² = ½ × 3.14 × 3² = ½ × 28.26 = 14.13 m²

📌 Step 3: Add them
Total = 60 + 14.13 = 74.13 ≈ 74.1 m²

💡 Strategy for composite figures: Always break them into shapes you know (rectangles, triangles, circles), calculate each, then add (or subtract for holes).

Question 7 of 10

TEKS 1A-1G Easy Calc Word

A pizza box is 14 inches on each side and 2 inches tall. What is the volume of the box?

A 280 in³

B 392 in³

C 196 in³

D 448 in³

Explanation

📌 Step 1: Identify the shape
A pizza box is a rectangular prism (cuboid).

📌 Step 2: Apply the volume formula
V = length × width × height
V = 14 × 14 × 2

📌 Step 3: Calculate
= 392 in³

💡 Quick check: Volume is always in cubic units. If your answer is in square units, something went wrong!

Question 8 of 10

TEKS 1A-1G Medium Calc Word Diagram

Quadrilateral ABCD has the properties shown below. Which type of quadrilateral is ABCD?

A Rectangle

B Rhombus

C Parallelogram

D Trapezoid

Explanation

A quadrilateral with exactly one pair of parallel sides is a trapezoid.
AB ∥ DC but AB ≠ DC (16 ≠ 22), confirming it is a trapezoid, not a parallelogram.

Question 9 of 10

TEKS 1A-1G Medium Calc Word Diagram

A kite is flying at the end of a 200-foot string. The string makes a 55° angle with the ground. How high above the ground is the kite? Round to the nearest foot. (sin 55° ≈ 0.819)

A 164 feet

B 141 feet

C 186 feet

D 115 feet

Explanation

📌 Step 1: Identify the trig ratio
We know the hypotenuse (200 ft) and want the opposite side (height).
Use sine: sin = opposite / hypotenuse

📌 Step 2: Set up and solve
sin(55°) = h / 200
0.819 = h / 200
h = 200 × 0.819 = 163.8

📌 Answer: ≈ 164 feet

💡 Tip: Angle of elevation from ground = angle between the string and the horizontal, NOT the vertical.

Question 10 of 10

TEKS 11A-11D Medium Calc Word Diagram

A swimming pool has the shape shown below — a rectangle with a semicircle on each end. Find the total area of the pool. (Use π ≈ 3.14)

A 200.0 m²

B 278.5 m²

C 257.0 m²

D 356.0 m²

Explanation

Rectangle area = 20 × 10 = 200 m².
Two semicircles = one full circle with r = 5: π × 5² = 3.14 × 25 = 78.5 m².
Total = 200 + 78.5 = 278.5 m².

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