Question

Triangle E F G. Side E F is 6 meters, F G is 5 meters, E G is 7 meters. Angle F is 87 degrees and angle G is 58 degrees. Triangle K L J. Side K L is 28 meters, L J is 24 meters, J K is 20 meters. Angle K is 58 degrees, L is 35 degrees, J is 87 degrees. What can you conclude about these triangles? Check all that apply. Angle E corresponds to angle L. All corresponding angles are proportional. The measure of angle E is 29°. The two triangles are similar. The two triangles are congruent.

Answer 1

Angle E corresponds to angle L

The two triangles are similar

Explanation:

Answer 2

Angle E corresponds to angle L

The two triangles are similar

Explanation:

The information given has been sketched in a diagram attached below.

✔️In ∆EFG:

EF = 6 m

FG = 5 m

EG = 7 m

<F = 87°

<G = 58°

<E = 180 - (87° + 58°) (sum of triangles)

<E = 35°

✔️In ∆KLJ:

KL = 28 m

LJ = 24 m

JK = 20 m

<K = 58°

<L = 35°

<J = 87°

✔️Let's compare both triangles:

<K = <G = 87° (corresponding angles)

Therefore, length of the sides opposite each angle corresponds to each other, which is:

LJ corresponds to EF, hence:

LJ/EF = 24/6 = 4 (corresponding sides are proportional)

<J = <F = 87° (corresponding angles)

KL corresponds to EG, hence:

KL/EF = 28/7 = 4 (both sides are proportional)

<L = <E = 35° (corresponding angles are equal)

JK corresponds to FG, hence:

JK/FG = 20/5 = 4 (both sides are proportional).

As we can see from the above, all three angles of both triangles are congruent/equal to each other. This means they have the same shape.

Also, all three corresponding sides of both triangles are proportional. This means they have different sizes.

Therefore, we can conclude that both triangles are similar to each other because they have corresponding angles that are equal, while their corresponding sides are proportional.

The following statements therefore apply:

Angle E corresponds to angle L

The two triangles are similar