It is given that triangle ABC is congruent triangle FDE and AB = 6 cm, angleB = 40° and angleA = 80°. What is length of side
DF of triangle FDE and its angleE?
Answers
Step-by-step explanation:
GIVEN
Triangle ABC is congruent to triangle FDE
AB = 6 cm
\sf{ \angle \: B = {40}^{ \circ} \: \: \: and \: \: \: \angle \: A = {80}^{ \circ} }∠B=40
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and∠A=80
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TO DETERMINE
1. The length of side DF of triangle FDE
\sf{ 2. \: \: \angle E }2.∠E
CONCEPT TO BE IMPLEMENTED
If two triangles are congruent then the corresponding sides are equal in length and the corresponding angles are equal in size for the two triangles
CALCULATION
We know that Sum of the three angles in a triangle is 180°
Hence
\sf{ \angle \: A +\angle \: B + \angle \: C = {180}^{ \circ} }∠A+∠B+∠C=180
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\implies \sf{ {80}^{ \circ} + {40}^{ \circ} + \angle \: C = {180}^{ \circ} }⟹80
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+40
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+∠C=180
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\implies \sf{ \angle \: C = {60}^{ \circ} }⟹∠C=60
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Since triangle ABC is congruent to triangle FDE
So the corresponding sides are equal in length and the corresponding angles are equal in size for the two triangles ABC and FDE
\therefore \: \: \sf{ \angle \: E = \angle C \: = {60}^{ \circ} }∴∠E=∠C=60
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\sf{DF = AB = 6 \: cm}DF=AB=6cm
RESULT
\boxed{ \: \: \: \sf{ \angle \: E = {60}^{ \circ} } \: \: and \: \: \: \: DF = 6 \: cm \: \: \: \: }
∠E=60
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andDF=6cm
Hope this will help you
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