# NCERT Mathematics Class 9 Exemplar Ch 7 Triangles Part 6

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**Exercise 7.4**

Q.1. Find all the angles of an equilateral triangle.

Answer:

Q.2. The image of an object placed at a point A before a plane mirror LM is seen at the point B by an observer at D as shown in Fig. Prove that the image is as far behind the mirror as the object is in front of the mirror.

Q.3. ABC is an isosceles triangle with and D is a point on BC such that (Fig. 7.13). To prove that, a student proceeded as follows:

In ∆ ABD and ∆ ACD, (Given) (because) and Therefore, ∆ ABD ≅ ∆ ACD (AAS)

So, (CPCT) what is the defect in the above arguments?

Answer: It is defective to use for proving this result.

Q.4. P is a point on the bisector of ∠ABC. If the line through P, parallel to BA meets BC at Q, prove that BPQ is an isosceles triangle.

Q.5. ABCD is a quadrilateral in which and. Show that BD bisects both the angles ABC and ADC.

Q.6. ABC is a right triangle with. Bisector of ∠A meets BC at D. Prove that

Q.7. O is a point in the interior of a square ABCD such that OAB is an equilateral triangle. Show that ∆ OCD is an isosceles triangle.

Q.8. ABC and DBC are two triangles on the same base BC such that A and D lie on the opposite sides of BC, and Show that AD is the perpendicular bisector of BC.

Q.9. ABC is an isosceles triangle in which AD and BE are respectively two altitudes to sides BC and AC. Prove that

Q.10. Prove that sum of any two sides of a triangle is greater than twice the median with respect to the third side.