Geometry — Semester B Practice

Question 1 of 10

TEKS 3A-3DHard 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 1A-1GMedium 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)

A186 feet

B164 feet

C141 feet

D115 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 3 of 10

TEKS 12A-12EMedium 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?

B14

C12

D10

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 4 of 10

TEKS 1A-1GHard 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)

A74.1 m²

B64.7 m²

C102.5 m²

D88.3 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 5 of 10

TEKS 1A-1GMedium Calc Word Diagram

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

ARectangle

BTrapezoid

CRhombus

DParallelogram

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 6 of 10

TEKS 11A-11DMedium Calc Word Diagram

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

A565.2 cm³

B1695.6 cm³

C452.2 cm³

D339.1 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 7 of 10

TEKS 11A-11DMedium 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)

A200.0 m²

B278.5 m²

C257.0 m²

D356.0 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.

Question 8 of 10

TEKS 1A-1GEasy Calc Word

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

A392 in³

B280 in³

C196 in³

D448 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 9 of 10

TEKS 1A-1GEasy 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)

A226.08 ft³

B75.36 ft³

C150.72 ft³

D301.44 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 10 of 10

TEKS 3A-3DEasy Calc Word Diagram

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

AD (Arrow)

BB (Regular hexagon)

CC (Parallelogram)

DA (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.

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