Q1 of 70 Page 139

∠B is a right angle in ΔABC and is an altitude to hypotenuse. AB = 8, BC = 6. Find the area of ΔBDC.

In ∆ABC, ∠B is a right angle, AB = 8 and BC = 6

= 24 …(1)

In ∆ABC, ∠B is a right angle and BD is an altitude,

In ∆ABC,

∠A + ∠C = 90⁰ and,

In ∆BDC,

∠DBC + ∠C = 90⁰

So, ∠A = ∠DBC …(2)

In ∆ABC and ∆BDC,

∠DAB ≅ ∠DBC [from (2)]

∠ADB ≅ ∠BDC [by right angles]

The correspondence ADB ↔ BDC is a similarity by AA corollary.

Areas of similar triangles are proportional to the squares of their corresponding sides.

…(3)

Now, ADB + BDC = ABC

BDC = 8.64

The area of ∆BDC is 8.64.

More from this chapter

All 70 →

In Δ ABC, Δ PQR and ΔXYZ correspondences ABC ↔ PQR, PQR ↔ XYZ are similarity. Prove that ABC ↔ XYZ is similarity.

State giving reasons, whether the following statements are true or false: In all the following questions the line does not contain a side of the triangle.

(1) A line can be drawn in the plane of a triangle not intersecting any of the sides of a triangle.

(2) A line can be drawn in the plane of a triangle which is not passing through any of the three vertices and intersecting all the three sides of the triangle.

(3) If a line drawn in the plane of a triangle intersects the triangle at only one point, the line passes through a vertex of the triangle.

(4) If a line intersects two of the three sides of a triangle in two distinct points and does not intersect the third side, then the line is parallel to the third side.

(5) In the plane of Δ ABC, a line / can be drawn such that = {P}, = {Q} and = ϕ.