If ABCD is a trapezium in which AB || CD and AD = BC, then:a. ∠A = ∠Bb. ∠A > ∠Bc. ∠A < ∠Bd. None of the above
Question
If ABCD is a trapezium in which AB || CD and AD = BC, then:a. ∠A = ∠Bb. ∠A > ∠Bc. ∠A < ∠Bd. None of the above
Solution
The answer is a. ∠A = ∠B.
Here's the step by step explanation:
- In trapezium ABCD, AB || CD and AD = BC.
- According to the properties of a trapezium, the angles on the same side of a leg are supplementary. Therefore, ∠A + ∠B = 180° and ∠C + ∠D = 180°.
- Given that AD = BC, triangle ABD is congruent to triangle BAC by the Side-Angle-Side (SAS) postulate. This means ∠A = ∠B.
- Therefore, the correct answer is a. ∠A = ∠B.
Similar Questions
ABCD is a trapezium in which AB||DC and AD = BC. If P, Q, R, S be respectively the mid points of BA, BD, CD and CA, then PQRS is a
ABC is an isosceles triangle with AB = AC and AD ⊥ BC. Is ∆ADB ≅ ∆ACD ?
ABCD is a trapezium and P, Q are the mid points of the diagonals AC and BD respectively. Then PQ is equal to
ABC is an isosceles triangle with AB = AC. Draw AP BC to show that ∠B = ∠C
In the right triangle, B is a point on AC such that .AB AD BC CD+ = + If ,AB x BC h= = and ,CD d= thenfind x (in term of h and d).
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.