The congruence of the angles and triangles are proven as follows;
a. The composition angles of FGH are alternate interior angles to the composition angles of angle AHEF
b. The three sides of triangle ∆EHG are congruent to the three sides of triangle ∆GFE, therefore, triangles ∆EHG and ∆GFE are congruent by SSS congruency rule
<h3>What are congruent triangles?</h3>
The lengths of the three sides of triangles that are congruent.
a. The shape of quadrilateral EFGH = A parallelogram
The measure of angle HEF = 90°
Angle HEF = 90°
Angle HEF = Angle HED + Angle DEF
Angle HED is congruent to angle FGD (Alternate interior angles theorem)
Angle HED = angle FGD
Angle DEF is congruent to angle DGH (Alternate interior angles theorem)
Angle DEF = angle DGH
Angle FGH = Angle FGD + Angle DGH
Angle FGH = Angle HED + Angle DEF (Substitution property)
Angle FGH = Angle HEF (Transitive property)
Angle FGH = Angle HEF = 90°
Therefore, the statement that will help prove angle FGH is also a right is that angle FGH is the sum of angles FGD and angle DGH which are alternate interior angles to angles HED and DEF which makes up angle HEF, which is a right angle.
b. The two-column method can be used to prove that triangle EHG and triangle GFE are congruent as follows;
Statement. Reason
EF is congruent to HG. Opposite sides of a parallelogram are congruent
EH is congruent FG Opposite sides of a parallelogram are congruent
EG is congruent to EG Reflexive property of congruency
∆EHG is cong. to ∆GFE SSS, Side-Side-Side, congruency rule
Learn more about the triangle congruency rules here:
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which means 12 is the perpendicular & 37 is the hypotenuse [ Since Sin θ =
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. Just plug the values :