ABC is a right angled isosceles triangle in which ∠A = 90°. If D and E are the mid-points of AB and AC respectively, then ∠ADE =
30°
45°
60°
90°

Question

ABC is a right angled isosceles triangle in which ∠A = 90°. If D and E are the mid-points of AB and AC respectively, then ∠ADE = 1. 30° 2. 45° 3. 60° 4. 90°

KnowledgeBoat · Accepted Answer

Given, ABC is a right angled isosceles triangle. Since, hypotenuse is the largest side thus other two sides of triangle will be equal. AC = AB ⇒ ∠C = ∠B = x (let) In △ABC, ⇒ ∠A + ∠B + ∠C = 180° ⇒ 90° + x + x = 180° ⇒ 2x = 180° - 90° ⇒ 2x = 90° ⇒ x = ⇒ x = 45° ⇒ ∠C = ∠B = 45° By mid-point theorem, The line segment joining the mid points of any two sides of a triangle is parallel to the third side and is equal to half of it. Since, D and E are the mid-points of AB and AC respectively. DE || BC AB is the transversal. ⇒ ∠ABC = ∠ADE (Corresponding angles are equal) ⇒ ∠ADE = 45°. Hence, option 2 is the correct option.

Mathematics

ABC is a right angled isosceles triangle in which ∠A = 90°. If D and E are the mid-points of AB and AC respectively, then ∠ADE =
30°
45°
60°
90°

Mid-point Theorem

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Mathematics

ABC is a right angled isosceles triangle in which ∠A = 90°. If D and E are the mid-points of AB and AC respectively, then ∠ADE =30°45°60°90°

Mid-point Theorem

Related Questions

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ABC is a right angled isosceles triangle in which ∠A = 90°. If D and E are the mid-points of AB and AC respectively, then ∠ADE =
30°
45°
60°
90°

BP and CQ are two medians of a △ABC. If QP = 4 cm, then BC =
2 cm
6 cm
8 cm
9 cm

On the sides AB and AC of a △ABC, D and E are two points such that AD : AB = AE : AC = 1 : 2. If BC = 7 cm, then DE =
3.5 cm
7 cm
14 cm
15 cm

AD and BE are two medians of a ABC. F is a point on AC such that DF || BE. If AC = 12 cm, then FC =
6 cm
4 cm
3 cm
none of these