Grade 10 · Geometry

Grade 10 Geometry questions and answers

The algebra, geometry, and SAT items US students search most. Written in American English for students, parents, and teachers in the United States.

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Practice quiz

Question and answer list

Open a card to see the answer. These are original practice items for US elementary students — not a state test copy.

1. Vertical angles are

Answer: congruent

They are opposite when two lines cross.

2. A straight angle measures

Answer: 180°

A line is a straight angle.

3. The sum of angles in a triangle is

Answer: 180°

A quadrilateral sums to 360°.

4. If two parallel lines are cut by a transversal, alternate interior angles are

Answer: congruent

They sit inside the parallels on opposite sides of the transversal.

5. A right angle measures

Answer: 90°

Perpendicular lines form right angles.

6. Complementary angles add to

Answer: 90°

Supplementary angles add to 180°.

7. An isosceles triangle has

Answer: at least two congruent sides

Base angles are congruent.

8. CPCTC is used after you

Answer: prove two triangles congruent

Corresponding parts of congruent triangles are congruent.

9. SOHCAHTOA: sine is

Answer: opposite / hypotenuse

Sin = O/H.

10. Cosine is

Answer: adjacent / hypotenuse

Cos = A/H.

11. Tangent is

Answer: opposite / adjacent

Tan = O/A.

12. In a right triangle, the hypotenuse is

Answer: the longest side, opposite 90°

Never use a leg as the hypotenuse in SOHCAHTOA.

13. If sin θ = 3/5, a possible opposite side is

Answer: 3 (with hypotenuse 5)

Keep the ratio.

14. A 30°-60°-90° triangle has sides

Answer: x, x√3, 2x

The side opposite 30° is the shortest.

15. A 45°-45°-90° triangle has legs

Answer: equal, and hypotenuse leg√2

It is isosceles.

16. To find an angle from two sides, use

Answer: inverse trig (sin⁻¹, cos⁻¹, tan⁻¹)

Calculators have SIN⁻¹.