Practice30Create account

In ΔABC, D is the midpoint of BC and AD ⊥ BC. Which statement is correct?

Class 9Triangles (Congruence)Geometry — Triangles
  • AAB = AC, so the triangle is isosceles
  • BAB = BC, so the triangle is equilateral
  • CThe triangle must be scalene
  • DNo conclusion is possible

Step-by-Step Solution

In ΔABD and ΔACD: BD = DC (D midpoint), ∠ADB = ∠ADC = 90° (AD ⊥ BC), AD = AD (common). By SAS, the triangles are congruent, so AB = AC (CPCT) and ΔABC is isosceles.
Answer: A) AB = AC, so the triangle is isosceles

Key idea: Isosceles triangle properties

**Theorem**: Angles opposite equal sides of an isosceles triangle are equal.

In ΔABC if AB = AC, then ∠B = ∠C.

**Proof sketch**: Drop a median (or angle bisector) from A to BC, meeting at D.
- AB = AC (given), AD = AD (common), BD = DC (median).
- By SSS, ΔABD ≅ ΔACD.
- By CPCT, ∠B = ∠C. ✓

**Converse**: Sides opposite equal angles are equal. (∠B = ∠C → AB = AC.)

Master this chapter in 30 minutes a day.

Don't just memorise the answer — build a daily practice habit.

Practice 5 Similar Questions Free →

All Triangles (Congruence) practice questions

More Class 9 Triangles (Congruence) practice

Two sides of a triangle measure 12 cm and 5 cm. Which of the following cannot be the…Look at the matching marks on the two triangles. Which congruence rule shows that △ABC ≅…The arcs and tick marks show which parts of △DEF and △LMN are equal. Which congruence…Both triangles have a right angle (square marks). Using the tick marks, which rule…The tick marks show that the three sides of △ABC are equal to the three sides of the…