Practice test

Basic geometry - Test Set 1

Review 20 exam-focused questions with detailed explanations, then start the interactive test when you are ready.

20 questions

Questions and explanations

  1. Question 1

    When two transversals intersect three parallel lines, and the ratio of the intercepts formed by the first transversal is 3 : 4, then find the ratio of the intercepts formed by the second transversal.
    1. 1 : 1
    2. 4 : 3
    3. 3 : 4
    4. 2 : 4
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  2. Question 2

    Find the degree measure of the angle subtended by an arc of length 22 cm at the center of a circle of radius 100 cm.
    1. 2° 36′
    2. 62° 36′
    3. 12° 36′
    4. 22° 36′
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  3. Question 3

    A pair of parallel lines is intersected by a transversal in such a way that ∠1 and ∠2 form alternate internal pairs. If m∠1 = 35°, then what is the measure of m∠2?
    1. 35°
    2. 145°
    3. 55°
    4. 65°
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  4. Question 4

    If the ratio of two interior angles lying on the same side of a transversal intersecting two parallel lines is 3 : 7, then find the positive difference of the measures of these two interior angles.
    1. 54°
    2. 80°
    3. 72°
    4. 64°
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  5. Question 5

    AB is parallel to CD. A transversal PQ intersects AB and CD at E and F respectively, and ∠PEB = 78°. G is a point between AB and CD such that ∠BEG = 18° and ∠GFE = 30°. What is the measure of ∠EGF?
    1. 72°
    2. 58°
    3. 66°
    4. 68°
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  6. Question 6

    In ΔABC, BD ⟂ AC, and ∠DBC = 44°. E is a point on BC such that ∠CAE = 34°. Find the measure of ∠AEB.
    1. 78°
    2. 80°
    3. 56°
    4. 46°
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  7. Question 7

    If the angles (3x − 5)° and 80° form a pair of supplementary angles, then find the value of x.
    1. 35°
    2. 45°
    3. 50°
    4. 90°
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  8. Question 8

    The difference of value of two complementary angles is 24°. Find the measure of the larger angle?
    1. 55°
    2. 33°
    3. 57°
    4. 43°
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  9. Question 9

    AB and CD are parallel lines of a circle with centre O. Points P and Q are on AB and CD respectively, such that PQ touches the circle at R. Then find the measure of ∠POQ.
    1. 85°
    2. 90°
    3. 80°
    4. 100°
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  10. Question 10

    If AB = x + 3, BC = 2x and AC = 4x − 5, then for what value of 'x' will B lies on AC?
    1. 2
    2. 5
    3. 8
    4. 3
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  11. Question 11

    The measures of the sides of a triangle are 15 cm, 28 cm and 41 cm. What is the length of the perpendicular corresponding to the 28 cm long side?
    1. 10 cm
    2. 14 cm
    3. 12 cm
    4. 9 cm
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  12. Question 12

    In triangle ABC, P, Q and R are the midpoints of its sides AB, CA and BC respectively. If the area of triangle PQR is 6 cm², then find the area of triangle ABC.
    1. 36 cm²
    2. 12 cm²
    3. 24 cm²
    4. 18 cm²
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  13. Question 13

    In triangle ABC, AD is the median of the triangle, which intersects BC at D. All three medians of the triangle meet at point G. If AG = (7y − 3) cm and DG = 3y cm, then find the length of AD.
    1. 33 cm
    2. 24 cm
    3. 30 cm
    4. 27 cm
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  14. Question 14

    Triangle ABC is an equilateral triangle. P, Q and R are the midpoints of the sides AB, BC and AC respectively. The length of the side of triangle is 4 cm. What will be the area of triangle PQR?
    1. 19cm2
    2. 39cm2
    3. 3 cm2
    4. 143 cm2
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  15. Question 15

    In ∠ABC, ∠A = 90°, AB = 6 cm, AC = 8 cm. If AD is perpendicular to BC, then find the value of AD?
    1. 4.6 cm
    2. 4.4 cm
    3. 4.8 cm
    4. 3.8 cm
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  16. Question 16

    If one angle of a triangle is equal to the sum of the other two angles, then the triangle is:
    1. An obtuse triangle
    2. An equilateral triangle
    3. An isosceles triangle
    4. A right triangle
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  17. Question 17

    In triangle ABC, if ∠ABC = 90° and BA = BC, then angles A and C will be respectively:
    1. 50°, 40°
    2. 45°, 45°
    3. 80°, 60°
    4. 80°, 70°
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  18. Question 18

    D and E are the midpoints of sides AB and AC of a triangle ABC, respectively, and BC = 6 cm. If DE ∥ BC then find the length of DE.
    1. 2.5 cm
    2. 3 cm
    3. 5 cm
    4. 6 cm
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  19. Question 19

    In ΔABC, DE ∥ BC, intersecting AB at D and AC at E. AD : BD = 2 : 3 and the area of trapezium BDEC is 63 cm². What is the area of ΔADE?
    1. 14 cm²
    2. 12 cm²
    3. 28 cm²
    4. 42 cm²
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  20. Question 20

    The hypotenuse of a right triangle is 2 more than twice one of the sides, while the third side is 13 more than half the hypotenuse. Find the length of the median drawn on the hypotenuse.
    1. 15
    2. 18
    3. 17
    4. 20
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