Geometry (8)

Question 1

What is the sum of the interior angles of a triangle?

Answer 1

180°

Question 2

What is the sum of the interior angles of a quadrilateral?

Answer 2

360°

Question 3

Find the measure of the missing angle if two angles of a triangle are 50° and 60°.

Answer 3

180 - (50 + 60) = 70°

Question 4

What is the sum of the interior angles of a pentagon?

Answer 4

(5 - 2) × 180 = 540°

Question 5

What is the measure of each interior angle of a regular hexagon?

Answer 5

720 ÷ 6 = 120°

Question 6

Two angles are complementary. If one angle is 35°, what is the other?

Answer 6

90 - 35 = 55°

Question 7

Two angles are supplementary. If one angle is 110°, what is the other?

Answer 7

180 - 110 = 70°

Question 8

Reflect the point (3, 5) over the y-axis. What are the coordinates?

Answer 8

(-3, 5)

Question 9

Rotate the point (2, 4) 90° clockwise around the origin.

Answer 9

(4, -2)

Question 10

Translate the point (1, 2) by vector (3, -1). What are the new coordinates?

Answer 10

(1 + 3, 2 - 1) = (4, 1)

Question 11

Dilate the point (2, 3) with a scale factor of 2 from the origin.

Answer 11

(4, 6)

Question 12

Find the measure of an exterior angle of a regular octagon.

Answer 12

360 ÷ 8 = 45°

Question 13

A triangle has angles in the ratio 2:3:4. Find each angle.

Answer 13

Sum = 180, parts = 2+3+4=9, angle measures: 40°, 60°, 80°

Question 14

Name the transformation: Flipping a shape over a line.

Answer 14

Reflection

Question 15

Name the transformation: Sliding a shape without rotating or flipping.

Answer 15

Translation

Question 16

Name the transformation: Turning a shape around a point.

Answer 16

Rotation

Question 17

Name the transformation: Resizing a shape proportionally.

Answer 17

Dilation

Question 18

In a regular polygon, the sum of exterior angles is always what?

Answer 18

360°

Question 19

A rectangle has one angle of 90°. What are the other angles?

Answer 19

90°, 90°, 90° (all right angles)

Question 20

A right triangle has legs of length 3 cm and 4 cm. Find the hypotenuse.

Answer 20

c = 5 cm

c² = 3² + 4² = 9 + 16 = 25 → c = 5 cm

Question 21

A right triangle has one leg of 6 cm and a hypotenuse of 10 cm. Find the other leg.

Answer 21

b = 8 cm

b² = 10² - 6² = 100 - 36 = 64 → b = 8 cm

Question 22

The hypotenuse of a right triangle is 13 cm and one leg is 5 cm. Find the other leg.

Answer 22

b = 12 cm

b² = 13² - 5² = 169 - 25 = 144 → b = 12 cm

Question 23

A right triangle has legs of length 7 cm and 24 cm. Find the hypotenuse.

Answer 23

c = 25 cm

c² = 7² + 24² = 49 + 576 = 625 → c = 25 cm

Question 24

Explain how the Pythagorean theorem can be used to check if a triangle with sides 5 cm, 12 cm, and 13 cm is a right triangle.

Answer 24

Yes, it’s a right triangle

Check if 5² + 12² = 13² → 25 + 144 = 169 → 13² = 169