MATH SOLVE

3 months ago

Q:
# 1. ΔEFG ~ ΔLMN. Find LN.A) 2.5 B) 3 C) 3.5 D) 5 2.suppose that m∠A = m∠D. Which other fact would guarantee that the triangles are SIMILAR?A) ABDE = CBFEB) m∠C = m∠F C) m∠A + m∠B + m∠C = 180° D) 180° - m∠D = m∠E + m∠F 3. Given that the two triangles shown are congruent, explain one way to verify that the corresponding angles of the two triangles are congruent.A) translate triangle 2 up 2 units, and to the left 6 units B) translate triangle 2 up 2 units, and to the right 6 units C) translate triangle 2 down 2 units, and to the left 6 units D) translate triangle 2 down 2 units, and to the right 6 units4. Trapezoid ABCD and trapezoid JKLM are similar. What side corresponds to side AB?A) side JM B) side JK C) side ML D) side DC

Accepted Solution

A:

Part 1:

Given that triangle EFG is similar to triangle LMN, this means that the ratio of the measures of any two sides of triangle EFG is equal to the ratio of the measures of the corresponding sides of triangle LMN.

From the figure shown

FG / EG = MN / LN

⇒ 4 / 7 = 2 / LN

⇒ LN = 7 * 2 / 4 = 14 / 4 = 3.5

Therefore, LN = 3.5

Part 2:

Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion.

Thus, if m∠A = m∠D. The other fact that would guarantee that the triangles are similar is that m∠C = m∠F.

This is because if m∠A = m∠D and m∠C = m∠F, then m∠B = m∠E and thus satisfies the triangle similarity condition.

Part 3:

Given that the two triangles shown are congruent, one way to verify that the corresponding angles of the two triangles are congruent is to place one of the triangle on top of the other to see if the corresponding angles of both triangles coincide.

This can be achieved by translating triangle 2 up by 2 units, and to the left by 6 units.

Part 4:

Given that trapezoid ABCD and trapezoid JKLM are similar.

From the naming of the trapezoids, the order of the naming of any similar object corresponds to the order of their similarity.

Thus, side AB corresponds to side JK, side AC corresponds to side JL and so on.

Therefore, the side that corresponds to side AB is side JK.

Given that triangle EFG is similar to triangle LMN, this means that the ratio of the measures of any two sides of triangle EFG is equal to the ratio of the measures of the corresponding sides of triangle LMN.

From the figure shown

FG / EG = MN / LN

⇒ 4 / 7 = 2 / LN

⇒ LN = 7 * 2 / 4 = 14 / 4 = 3.5

Therefore, LN = 3.5

Part 2:

Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion.

Thus, if m∠A = m∠D. The other fact that would guarantee that the triangles are similar is that m∠C = m∠F.

This is because if m∠A = m∠D and m∠C = m∠F, then m∠B = m∠E and thus satisfies the triangle similarity condition.

Part 3:

Given that the two triangles shown are congruent, one way to verify that the corresponding angles of the two triangles are congruent is to place one of the triangle on top of the other to see if the corresponding angles of both triangles coincide.

This can be achieved by translating triangle 2 up by 2 units, and to the left by 6 units.

Part 4:

Given that trapezoid ABCD and trapezoid JKLM are similar.

From the naming of the trapezoids, the order of the naming of any similar object corresponds to the order of their similarity.

Thus, side AB corresponds to side JK, side AC corresponds to side JL and so on.

Therefore, the side that corresponds to side AB is side JK.