A set of small building blocks contains 48 blocks. The blocks are cube-shaped and have an edge length of 1/2 inch. If all the bl
1 answer:
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Step-by-step proof:
Check the attached picture
Statement - Reason
Parallelogram ABCD - Given
Line AC - two points determine a line
AB║CD ; AD║BC - A parallelogram has 2 pairs of opposite sides parallel
∠1 ≅ ∠4 ; ∠2 ≅ ∠3 - line AC acts as a transversal for the parallel sides therefore, they are congruent through alternate interior angles
Line AC ≅ Line AC - Reflexive property
ΔABC ≅ ΔCDA - ASA (Angle - Side - Angle postulate)
∠D = ∠B - CPCTC (Corresponding Parts of Congruent Triangles are Congruent)
m∠1 = m∠4 ; m∠2 = m∠3 - Congruent angles have congruent measures
m∠1 + m∠2 = m∠3 + m∠4 - Addition property of equality
m∠1 + m∠2 = m∠DAB m∠3 + m∠4 = m∠BCD - Angle Addition Postulate
m∠DAB = m∠BCD - Substitution
∠DAB = ∠BCD - Congruent angles have equal measures.
Hope this helps :)
