Sides Opposite Equal Angles (Motivate) MCQs Quiz | Class 9
This quiz targets Class IX Mathematics (Code 041), Unit IV: Geometry, specifically addressing the converse isosceles property where sides opposite to equal angles are equal. Please complete the 10 multiple-choice questions below, click submit to view your detailed results, and download the solution PDF for your records.
Overview: Sides Opposite Equal Angles
In Class 9 Geometry, we explore the properties of triangles. One fundamental theorem is the Converse of the Isosceles Triangle Property. This theorem motivates the understanding that geometric equality works both ways: just as equal sides imply equal angles, equal angles imply equal sides.
The Theorem Statement
“The sides opposite to equal angles of a triangle are equal.”
This means if you have a triangle ABC where angle B is equal to angle C, then the side opposite angle B (which is AC) is equal to the side opposite angle C (which is AB). Thus, AB equals AC.
Key Concepts & Proof Motivation
- Motivation: To prove this, we typically construct an angle bisector from vertex A to side BC and use triangle congruence criteria (like AAS or ASA).
- Isosceles Triangle: A triangle with two equal angles is always an isosceles triangle.
- Equilateral Triangle: If all three angles are equal (60 degrees each), then all three sides are equal, making it equilateral.
Comparison Table
| Given Condition | Conclusion | Property Name |
|---|---|---|
| AB = AC (Sides are equal) | Angle C = Angle B | Isosceles Triangle Property |
| Angle B = Angle C (Angles are equal) | AC = AB | Converse Property |
Extra Practice Questions
- In triangle PQR, if angle P = 45 degrees and angle Q = 45 degrees, which two sides are equal? (Answer: PR and QR)
- Can a triangle have two equal angles of 90 degrees? (Answer: No, sum would be 180 without the third angle)
- If one angle of a right-angled triangle is 45 degrees, is the triangle isosceles? (Answer: Yes)
- In an equilateral triangle, are sides opposite equal angles equal? (Answer: Yes, all sides are equal)
- If angle A = 70 degrees and angle B = 70 degrees in triangle ABC, find AC if BC = 10cm. (Answer: AC = 10cm)
