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jekas [21]
3 years ago
14

Can someone please help me

Mathematics
1 answer:
mina [271]3 years ago
4 0

Answer:

The value of x is 7

AC congruent to DF because AC = 13.5 in. and DF = 13.5 in, EF congruent to BC because EF = 12 in. and BC = 12 in., ∠C congruent to ∠F. The triangles ACB and DEF congruent by the SAS Triangle Congruence Theorem only when x = 7

Step-by-step explanation:

<em>If two sides in a triangle congruent to two sides in other triangle and the including angles between the two sides are congruent in the triangles, then the two triangles are congruent by the SAS postulate of congruency</em>

In the given figure

→ If ∠C ≅ ∠F

∵ m∠C = m∠F

∵ m ∠ C = (2x + 14)°

∵ m∠F = (4x)°

→ Equate them to find x

∴ 4x = 2x + 14

→ Subtract 2x from both sides

∴ 2x = 14

→ Divide both sides by 2

∴ x = 7

→ In Δs ABC and DEF

∵ AC congruent to DF because AC = 13.5 in. and DF = 13.5 in

∵ EF congruent to CB because EF = 12 in. and CB = 12 in.

∵ ∠C congruent to ∠F

∴ The triangles ACB and DEF congruent by the SAS Triangle Congruence

   Theorem only when x = 7

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Answer:

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Step-by-step explanation:

This is an isosceles triangle, therefore, the angles that are across from the congruent sides are also congruent:  x = y

We also know that by the Triangle Angle Sum Theorem, that all the angles of the triangle add up to equal 180 degrees.

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