Find AH, in the roof truss shown AB=8 and m\angle HAF=37^{\circ}. The roof truss has line symmetry.

alesterp

alesterp

Answered question

2021-07-20

In the roof truss shown, AB=8 and mHAF=37.
Find: AH
Given:
AB=8 and mHAF=37.
The roof truss has line symmetry.

Figure(1)

Answer & Explanation

Clelioo

Clelioo

Skilled2021-07-21Added 88 answers

Approach:
(1) If a figure has line symmetry then one side of the symmetric line is congruent to the other side of the line.
(2) If two triangles are congruent to each other then all sides of the triangle are congruent.
Calculation:
The roof truss has line symmetry about line over{AE}.
So,
ABD=AHF.
Use transitive property of congruence.
ABD=AHF and AH, and AB are the sides of congruent triangles.
So,
AH=AB
Substitute 8 for AH in order to find the value of AH.
AH=8
Conclusion:
Therefore, the value of AH is 8.

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