Attempt following question by selecting a choice to answer.
D
What is the measure of
∠A, if
ΔABC is congruent to
ΔDEF?BBBB DDDDA.
D45
oB.
D55
oC.
D30
oD.
DNone of the above
DD
A
Step 1: In ΔDEF, m∠E = 90o and m∠F = 45o.
Step 2: Sum of the angles of a triangle is equal to 180o.
Step 3: m∠D + m∠E + m∠F = 180o
Step 4: m∠D + 90o + 45o = 180o[Substitute the measures of angles E and F.]
Step 5: m∠D + 135o = 180o[Simplify.]
Step 6: m∠D = 45o[Subtraction property for equality.]
Step 7: ΔABC is congruent to ΔDEF.
Step 8: So, the corresponding angles and sides of ΔABC and ΔDEF are equal.
Step 9: AB = DE, so, m∠F = m∠C[In congruent triangles, the angles opposite to the equal sides are equal. ]
Step 10: m∠B = m∠E so, m∠A = m∠D.
Step 11: m∠A = m∠D = 45o
Step 12: So, the measure of ∠A is 45o.