Question

Δ MAL and Δ DLA are right triangles. If Δ MAL ≅ ΔDLA, then side DL is congruent to side MA, and ∠ MAL is congruent to ∠ DLA. Given ∠ M is 30 °, side DL is (2x + 10) cm, side MA is (3x – 2) cm, and side AL is (x + 5) cm, answer the following questions below:

What is the measurement of DL?

What is the measurement of AL?

What is the measurement of ∠ DLA?

What is the measurement of ∠ AEL?

Answer 1

1. DL = 34 cm
2. AL = 17 cm
3. ∠DLA = 60°
4. ∠ADL = 30°

Explanation:

Given:

• DL = (2x + 10) cm
• MA = (3x - 2) cm
• DL ≅ MA

Equating DL and MA :

⇒ 2x + 10 = 3x - 2

⇒ 2x + 12 = 3x

⇒ x = 12

Finding DL and AL :

• DL = 2(12) + 10 = 24 + 10 = 34 cm
• AL = 12 + 5 = 17 cm

Finding ∠DLA :

• ∠M = ∠D = 30° (corresponding parts of congruent triangles)

• ∠DLA + ∠D + 90° = 180°
• ∠DLA + 30° = 90°
• ∠DLA = 60°

Finding ∠ADL :

• ∠ADL = ∠D

• ∠ADL = 30°

Answer 2

DL = 34 cm

AL = 17 cm

∠DLA = 60°

∠ADL = 30°

Explanation:

Given:

• DL = (2x + 10) cm
• MA = (3x - 2) cm

DL ≅ MA

⇒ 2x + 10 = 3x - 2

⇒ 2x + 12 = 3x

⇒ 12 = x

Substituting found value of x into expressions for DL and AL:

DL = 2x + 10

= 2(12) + 10

= 34 cm

AL = x + 5

= 12 + 5

= 17 cm

The only way for ΔMAL to be a right triangle, with MA = 34 cm, AL = 17 cm and ∠M = 30° is if

• MA is the hypotenuse
• AL is the shortest side

Given:

• ∠M = ∠D = 30°
• ∠MAL ≅ ∠DLA

Sum of interior angles of a triangle is 180°

⇒ ∠DLA + 30° + 90° = 180°

⇒ ∠DLA + 120° = 180°

⇒ ∠DLA = 60°

As ∠M = ∠D = 30°, then ∠ADL = 30°