Given, ΔABE ≅ ΔACD
∴ AB = AC [By (CPCT)] ……………………………….(i)
And, AD = AE [By (CPCT)] ……………………………(ii)
(CPCT - Corresponding parts of congruent triangle)
In ΔADE and ΔABC, dividing equation (ii) by (i)
$ \dfrac{AD}{AB} = \dfrac{AE}{AC}$
$\angle A = \angle A $ [Common angle]
ΔADE ~ ΔABC [SAS similarity criterion]
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In Fig. 6.38, altitudes AD and CE of Δ ABC intersect each other at the point P. Show that:
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E is a point on the side AD produced of a parallelogram ABCD and BE intersects CD at F. Show that Δ ABE ~ Δ CFB. |
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In Fig. 6.39, ABC and AMP are two right triangles, right angled at B and M respectively. Prove that:
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CD and GH are respectively the bisectors of $\angle ACB$ and $\angle EGF$ such that D and H lie on sides AB and FE of Δ ABC and Δ EFG respectively. If Δ ABC ~ Δ FEG, show that: |
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In Fig. 6.40, E is a point on side CB produced of an isosceles triangle ABC with AB = AC. If AD ⊥ BC and EF ⊥ AC, prove that Δ ABD ~ Δ ECF.
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Sides AB and BC and median AD of a triangle ABC are respectively proportional to sides PQ and QR and median PM of Δ PQR (see Fig. 6.41). Show that Δ ABC ~ Δ PQR.
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D is a point on the side BC of a triangle ABC such that $\angle ADC = \angle BAC$. Show that $CA^2$ = CB.CD. |
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Sides AB and AC and median AD of a triangle ABC are respectively proportional to sides PQ and PR and median PM of another triangle PQR. Show that Δ ABC ~ Δ PQR. |
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A vertical pole of length 6 m casts a shadow 4 m long on the ground and at the same time a tower casts a shadow 28 m long. Find the height of the tower. |
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If AD and PM are medians of triangles ABC and PQR, respectively where Δ ABC ~ Δ PQR, prove that $\dfrac{AB}{PQ} = \dfrac{AD}{PM}$ |
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