Question
(a) In the given figure, show that ΔAMP≅ΔAMQ.
(b)
In the given figure, AC = CE and AB ∥ ED. The value of x is ___ units.
[4 MARKS]
Answer: Option A
:
Each part: 2 Marks
(a)
In ΔAMP and ΔAMQ,
PM=QM [Given]
∠AMP=∠AMQ [Given]
AM=AM [Common side]
⇒ΔAMP≅ΔAMQ [SAS congruency criteria]
(b)
In ΔABC and ΔEDC,AC=CE (given)∠BAC=∠DEC (since AB||DE and AE is a transversal, so they are alternate angles)∠ACB=∠ECD (vertically opposite angles)∴ΔABC≅ΔEDC (A.S.A. congruence criteria)∴AB=DE(sides of congruent triangles)∴x+10=2x−5⇒x−2x=−5−10⇒−x=−15⇒x=15 units
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:
Each part: 2 Marks
(a)
In ΔAMP and ΔAMQ,
PM=QM [Given]
∠AMP=∠AMQ [Given]
AM=AM [Common side]
⇒ΔAMP≅ΔAMQ [SAS congruency criteria]
(b)
In ΔABC and ΔEDC,AC=CE (given)∠BAC=∠DEC (since AB||DE and AE is a transversal, so they are alternate angles)∠ACB=∠ECD (vertically opposite angles)∴ΔABC≅ΔEDC (A.S.A. congruence criteria)∴AB=DE(sides of congruent triangles)∴x+10=2x−5⇒x−2x=−5−10⇒−x=−15⇒x=15 units
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