Maths-

General

Easy

Question

# Determine whether 𝐴𝐵 and 𝐶𝐷 are congruent. 𝐴 ≡ (3,4), 𝐵 ≡ (−2,4), 𝐶 ≡ (1, −3), 𝐷 ≡ (1,2).

Hint:

Distance between two points having coordinates (x

1

, y

1

) and (x

2

, y

2

) is given by formula:
- Distance
- AB and CD are congruent when AB = CD

- Distance between two points having coordinates (x

- , y

- ) and (x

- , y

- Distance
- AB and CD are congruent when AB = CD

## The correct answer is: AB and CD are congruent.

### Step by step explanation:

- Given:

𝐴 ≡ (3,4), 𝐵 ≡ (−2,4), 𝐶 ≡ (1, −3), 𝐷 ≡ (1,2).

- Step 1:
- Find AB:

Distance =

AB =

AB =

AB =

AB =

AB = 5

AB = 5 units.

- Step 2:
- Find CD:

Distance =

CD =

CD =

CD =

CD =

CD = 5

CD = 5 units.

It is clear that,

AB = CD

Hence, AB and CD are congruent.

- Given:

AB = 5 units.

CD = 5 units.

It is clear that,

AB = CD

Hence, AB and CD are congruent.

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