Criteria for Triangle Congruence

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Criteria for Triangle Congruence

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Important Questions

In triangles ABC and DEF, AB FD and . The two triangles will be congruent by
SAS axiom if :

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is an isosceles triangle with and and are its two medians. Show that .

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If in two triangles and , , and , then   ___.

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If is an isosceles triangle such that PQ=PR , then prove that the attitude PS from P on QR bisects QR

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A round balloon of radius r subtends an angle at the eye of the observer, while the angle of elevation of its centre is .  Prove that the height of the centre of the balloon is .

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In and and . Vertices and are joined to vertices and respectively. Show that
(i) Quadrilateral is a parallelogram
(ii) Quadrilateral is a parallelogram
(ii) and
(iv) Quadrilateral is a parallelogram
(v)
(vi)

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In an isosceles triangle , with , the bisectors of and intersect each other at . Join to . Show that :
(i) (ii) bisects

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is an isosceles triangle in which and are respectively two altitudes of side and . Prove that .

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Two triangles are congruent, if two angles and the side included between them in one triangle is equal to the two angles and the side included between them of the other triangle.This is known as

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In a triangle and , and . The two triangles will be congruent by SAS axiom if:

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