Question

In the figure Alongside ,AP and BP are the angular bisector of∡ BAD and ∡ABC respectively show that ∡APB ≡1 right angle triangle

Answer 1

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Answer 2

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7th

Maths

Congruence of Triangles

Criteria for Triangle Congruence

Let ABC be an acute - angle...

MATHS

Let ABC be an acute-angled triangle; AD be the bisector of ∠ BAC with D on BC; and BE be the altitude from B on AC. Find ∠ CED

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ANSWER

Draw DL perpendicular to AB; DK perpendicular to AC; and DM perpendicular to BE. Then EM = DK.

Since AD bisects ∠A, we observe that ∠ BAD =∠KAD. Thus in triangles ALD and AKD, we see that ∠LAD =∠KAD.

∠AKD = 90

∘

=∠ALD; and AD is common. Hence triangles ALD and AKD are congruent, giving DL = DK. But DL > DM, since BE lies inside the triangle (by acuteness property). Thus EM > DM.

This implies that ∠EDM>∠DEM=90

∘

−∠EDM.

We conclude that ∠EDM>45

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Since ∠CED=∠EDM

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