Question

# Which of the following relation is correct if AD = AC?

- AB < AD
- AB > AD
- AB = AD
- AB = AD

Hint:

### According to the properties of a triangle, the side opposite to larger angle is longer than the side opposite to the smaller angle and Angles opposite to equal sides are equal. using statement compare the two sides AB and AC of the triangle ABC.

## The correct answer is: AB > AD

### In ΔACD, AD = AC

⇒ ∠ADC = ∠ACD ————–(i) (Angles opposite to equal sides are equal)

⇒ ∠ADC = ∠ACB ————–(ii)

Since, the exterior angle of a triangle is greater than each of the interior opposite angles,

∠ADC > ∠ABD

⇒ ∠ACB > ∠ABC (From equation ii)

⇒ AB > AC (Side opposite to larger angle is the longer side in a triangle)

⇒ AB > AC (AD = AC).

### Related Questions to study

### Identify the rule by which the following triangles are congruent.

### Identify the rule by which the following triangles are congruent.

What does a translation do to an image?

Hence Translation does sliding of image.

What does a translation do to an image?

Hence Translation does sliding of image.

Which of the following triangles has no line of symmetry?

Which of the following triangles has no line of symmetry?

A type of transformation where a geometric figure slides horizontally, vertically, or both. What type of transformation is this?

A type of transformation where a geometric figure slides horizontally, vertically, or both. What type of transformation is this?

What is the order of rotational symmetry for the given figure?

What is the order of rotational symmetry for the given figure?

How is trapezoid ABCD translated to trapezoid A'B'C'D'?

A translation in which the size and shape of a graph of a function is not changed, but the location of the graph is.

How is trapezoid ABCD translated to trapezoid A'B'C'D'?

A translation in which the size and shape of a graph of a function is not changed, but the location of the graph is.