Answers in bold
- Statement 1: QUAD is an isosceles trapezoid
- Reason 2: Definition of isosceles trapezoid
- Reason 3: Reflexive Property of Congruence
- Statement 4: QA = DU
- Statement 5: Triangle DQU = Triangle AUQ
- Reason 6: CPCTC
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Step-by-step explanation:
- We always start a proof by repeating what is given. Do so word for word. It might seem silly to do this, but this is how all proofs are done in a formal manner.
- An isosceles trapezoid has the non-parallel sides equal to one another. Think of an isosceles triangle.
- Any segment is congruent to itself by the reflexive property. Think "reflection" in a mirror.
- The diagonals go from one corner to the opposite corner.
- Statements 1,2, and 3 help lead to statement 4 where we can conclude triangle DQU is congruent to triangle AUQ (by the SSS congruence theorem)
- The last reason is CPCTC, which stands for "corresponding parts of congruent triangles are congruent". It's like saying two cars are identical if they have the same engine. The car represents the overall triangle, while the engine represents the piece of the triangle. All of the corresponding pieces must match in order for the overall triangles to be cloned copies of each other.