Question

show the two pentagons are congruent find the side length of abcde and angle measures of fghij​

Answer 1

Two figures are congruent if the corresponding parts are congruent

1. ABCDE ≅ FGHIJ by the converse of Congruent Parts of Congruent Figures are Congruent

2. The side lengths of ABCDE are;

• BC = 1.4,       CD = 3.2,        ${}$   DE = 4.1,            EA = 2.8,            AB = 2.2

The angle measures of FGHIJ are;

• ∠IHG = 117°,   ∠HGF = 94°,    ${}$  ∠GFJ = 59°,       ∠FJI = 162°,   ∠JIH = 108°

Reason:

The two pentagons are congruent due to the attributes;

Analyzing the segments of ABCDE, and FGHIJ, in a clockwise manner, we have;

• Segments BC and IH are each diagonals of one square each

BC = IH

• Segments CD and HG are each diagonals of three squares in a row each

CD = HG

• Segments DE and GF are each diagonals of four squares in a row

DE = GF

• Segments EA and FJ are each diagonals of four squares arranged two by two

EA = FJ

• Segments AB and JI are each diagonals of two squares in a row

AB = JI

Therefore;

• ABCDE ≅ IHGFJ by the converse of Congruent Parts of Congruent Figures are Congruent, CPCFC congruency

2. From question 1., we have;

The side lengths of ABCDE from CPCFC

BC = IH = 1.4

• BC = 1.4

CD = HG = 3.2

• CD = 3.2

DE = GF = 4.1

• DE = 4.1

EA = FJ = 2.8

• EA = 2.8

AB = JI = 2.2

• AB = 2.2

The angle measure of FGHIJ by CPCFC

∠IHG = ∠BCD = 117°

• ∠IHG = 117°

∠HGF = ∠CDE = 94°

• ∠HGF = 94°

∠GFJ = ∠DEA = 59°

• ∠GFJ = 59°

∠FJI = ∠EAB = 162°

• ∠FJI = 162°

∠JIH = ∠ABC = 108°

• ∠JIH = 108°

Learn more about CPCFC here:

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