ABC is a triangle in which altitudes BE and CF to sides AC and AB are equal (see Fig. 7.32). Show that (i) △ ABE ≅ △ ACF (ii) AB = AC, i.e., ABC is an isosceles triangle.

AAS Congruence Rule for Triangles, Converse of Isosceles Triangle Theorem | PadhAiPro

Question

CASE_STUDIESAAS Congruence Rule for TrianglesConverse of Isosceles Triangle TheoremNCERT Textbook2 sub-questions

Similar Questions

Line-segment AB is parallel to another line-segment CD. O is the mid-point of AD (see Fig. 7.15). Show that (i) △AOB ≅ △DOC (ii) O is also the mid-point of BC.

CASE_STUDIESAAS Congruence Rule for Triangles

AD and BC are equal perpendiculars to a line segment AB (see Fig. 7.18). Show that CD bisects AB.

TextAAS Congruence Rule for Triangles

Line l is the bisector of an angle ∠ A and B is any point on l. BP and BQ are perpendiculars from B to the arms of ∠ A (see Fig. 7.20). Show that: (i) △ APB ≅ △ AQB (ii) BP = BQ or B is equidistant from the arms of ∠ A.

CASE_STUDIESAAS Congruence Rule for Triangles

In an isosceles triangle ABC, with AB = AC, the bisectors of ∠ B and ∠ C intersect each other at O. Join A to O. Show that: (i) OB = OC (ii) AO bisects ∠ A

CASE_STUDIESIsosceles Triangle Property of Equal AnglesConverse of Isosceles Triangle Theorem

ABC is an isosceles triangle in which altitudes BE and CF are drawn to equal sides AC and AB respectively (see Fig. 7.31). Show that these altitudes are equal.

TextAAS Congruence Rule for TrianglesIsosceles Triangle Property of Equal Angles

ABC is an isosceles triangle with AB = AC and D is a point on BC such that AD ⊥ BC (Fig. 7.13). To prove that ∠BAD = ∠CAD, a student proceeded as follows: In ∆ ABD and ∆ ACD, AB = AC (Given) ∠B = ∠C (because AB = AC) and ∠ADB = ∠ADC Therefore, ∆ ABD ≅ ∆ ACD (AAS) So, ∠BAD = ∠CAD (CPCT) What is the defect in the above arguments?

TextAAS Congruence Rule for Triangles