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Standard VII

Mathematics

ASA Criteria for Congruency

ABC is a tria...

Question

ABC is a triangle and D is the mid point of bc. The perpendiculars from D To AB and AC are equal prove that triangle is isosceles

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Solution

In triangles BEC BFC,

BE = CF (given)

angle CEB = angle BFC (90^o each)

BC = BC (common side)

.^.. triangle BEC is congruent to triangle BFC.(R-H-S)

Now, 1/2 CE + 1/2 CE = 1/2 BF + 1/2 BF (^..^.BF = CE)

= AC=AB

.^.. triangle ABC is isosceles.

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ABC is a triangle and D is the mid point of bc. The perpendiculars from D To AB and AC are equal prove that triangle is isosceles

In triangles BEC BFC, BE = CF (given) angle CEB = angle BFC (90o each) BC = BC (common side) ... triangle BEC is congruent to triangle BFC.(R-H-S) Now, 1/2 CE + 1/2 CE = 1/2 BF + 1/2 BF (...BF = CE) = AC=AB ... triangle ABC is isosceles.

In triangles BEC BFC,

BE = CF (given)

angle CEB = angle BFC (90^o each)

BC = BC (common side)

.^.. triangle BEC is congruent to triangle BFC.(R-H-S)

Now, 1/2 CE + 1/2 CE = 1/2 BF + 1/2 BF (^..^.BF = CE)

= AC=AB

.^.. triangle ABC is isosceles.