Home
Class 9
MATHS
In Delta ABC, the bisector AD of A is ...

In `Delta` ABC, the bisector AD of A is perpendicular to side BC (see Fig. 7.27). Show that `A B\ =\ A C`and `DeltaA B C`is isosceles

Text Solution

AI Generated Solution

To solve the problem, we need to show that in triangle ABC, where AD is the angle bisector of angle A and is perpendicular to side BC, the sides AB and AC are equal, thus proving that triangle ABC is isosceles. ### Step-by-Step Solution: 1. **Draw Triangle ABC**: - Begin by sketching triangle ABC. Label the vertices A, B, and C. 2. **Draw Angle Bisector AD**: ...
Promotional Banner

Topper's Solved these Questions

  • TRIANGLES

    NCERT ENGLISH|Exercise EXERCISE 7.5|4 Videos

  • TRIANGLES

    NCERT ENGLISH|Exercise EXERCISE 7.2|8 Videos

  • TRIANGLES

    NCERT ENGLISH|Exercise EXERCISE 7.1|8 Videos

  • SURFACE AREAS AND VOLUMES

    NCERT ENGLISH|Exercise Exercise 13.9|3 Videos

Similar Questions

Explore conceptually related problems

In Delta ABC , AD is the perpendicular bisector of BC (see Fig. 7.30). Show that Delta ABC is an isosceles triangle in which A B\ =\ A C .

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

In triangle ABC, AD is perpendicular to side BC and AD^2 = BD xx DC . Show that angle BAC = 90^@ .

In a Delta ABC , the median AD is perpendicular to AC. If b = 5 and c = 11, then a =

ABC and DBC are two isosceles triangles on the same base BC (see Fig. 7.33). Show that /_A B D\ =/_A C D

In quadrilateral ACBD, A C\ =\ A D and AB bisects /_A (see Fig. 7.16). Show that DeltaA B C~=DeltaA B D

D is a point on side BC of DeltaA B C such that A D\ =\ A C (see Fig. 7.47).Show that A B\ >\ A D .

In a triangle ABC, AB = BC, AD is perpendicular to side BC and CE is perpendicular to side AB. Prove that : AD = CE.

ABC is a triangle in which altitudes BE and CF to sides AC and AB are equal (see Fig. 7.32). Show that (i) DeltaA B E~=DeltaA C F (ii) A B\ =\ A C , i.e., ABC is an isosceles triangle.

In an isosceles triangle ABC with A B = A C , D and E are points on BCsuch that B E = C D (see Fig. 7.29). Show that A D= A E