If the non-parallel sides of a trapezium are equal, prove that it is cyclic.
Answers
Answered by
1
Step-by-step explanation:
⠀━━━━━━━━━━━━━━━━━━━━━━━━
If the non-parallel sides of a trapezium are equal, prove that it is cyclic.
⠀━━━━━━━━━━━━━━━━━━━━━━━━
ABCD is a trapezium where non-parallel sides AD and BC are equal.
∴DM and CN are perpendicular drawn on AB from D and C, respectively.
ABCD is cyclic trapezium.
In △DAM and △CBN,
∴AD = BC ... [Given]
∠AMD =∠BNC ...[Right angles]
∴DM = CN ...[Distance between the parallel lines]
∴Therefore, △DAM≅△CBN by RHS congruence condition.
⠀━━━━━━━━━━
Now, ∠A =∠B ...[by CPCT]
Also, ∠B+∠C=180° ....[Sum of the co-interior angles]
⠀━━━━━━━━━━
⠀━━━━━━━━━━
Thus, ABCD is a cyclic quadrilateral as the sum of the pair of opposite angles is 180°.
⠀━━━━━━━━━━━━━━━━━━━━━━━━
Please refer to the attachment also ❤️
⠀━━━━━━━━━━━━━━━━━━━━━━━━
Attachments:
Similar questions
Math,
1 month ago
Math,
1 month ago
Hindi,
1 month ago
English,
2 months ago
Computer Science,
2 months ago
World Languages,
8 months ago
Science,
8 months ago