Triangles – Theorems Quiz - ICSE Class 9 Mathematics
Free practice quiz: Triangles – Theorems (ICSE Class 9 Mathematics). 53 multiple-choice questions with answers and explanations. Play online, no sign-up needed.
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In triangle ABC, if AB = AC and angle BAC = 80 degrees, then what is the measure of angle ABC?
- 40 degrees
- 50 degrees
- 60 degrees
- 70 degrees
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Answer: B. 50 degrees
Since AB = AC, triangle ABC is an isosceles triangle. The angles opposite to equal sides are equal, so angle ABC = angle ACB. The sum of angles in a triangle is 180 degrees. Therefore, angle ABC + angle ACB + angle BAC = 180 degrees. 2 * angle ABC + 80 degrees = 180 degrees. 2 * angle ABC = 100 degrees. Angle ABC = 50 degrees.
In a triangle ABC, if angle A > angle B, then which side is longer?
- BC
- AC
- AB
- None of the above
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Answer: A. BC
The theorem states that in any triangle, the side opposite the larger angle is longer than the side opposite the smaller angle. Since angle A is greater than angle B, the side opposite angle A (which is BC) is longer than the side opposite angle B (which is AC).
If triangle ABC is congruent to triangle DEF (ABC ≅ DEF), which angle is equal to angle B?
- Angle D
- Angle E
- Angle F
- None of the above
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Answer: B. Angle E
When two triangles are congruent, their corresponding angles are equal. In the congruence statement ABC ≅ DEF, the order of vertices is important. Angle A corresponds to Angle D, Angle B corresponds to Angle E, and Angle C corresponds to Angle F. Therefore, Angle B = Angle E.
If triangle ABC and triangle DBC share the same base BC and lie between the same parallels AB and DC, then what is the relationship between their areas?
- Area(ABC) < Area(DBC)
- Area(ABC) > Area(DBC)
- Area(ABC) = Area(DBC)
- Area(ABC) is twice Area(DBC)
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Answer: C. Area(ABC) = Area(DBC)
Triangles on the same base and between the same parallels have equal areas. Since triangle ABC and triangle DBC share base BC and are between parallels AB and DC (assuming AB || DC), their heights with respect to the base BC are equal. Hence, their areas are equal.
Which of the following is NOT a criterion for congruence of triangles?
- SSS
- SAS
- AAA
- ASA
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Answer: C. AAA
SSS (Side-Side-Side), SAS (Side-Angle-Side), and ASA (Angle-Side-Angle) are valid congruence criteria. AAA (Angle-Angle-Angle) is not a congruence criterion because triangles with equal angles can be similar but not necessarily congruent (they can be of different sizes).