Final Answer:
c. Definition of midpoint
d. Definition of congruence
e. Reflexive Property
f. SSS Congruence Postulate
g. CPCTC
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Explanation:
Let’s go step by step for problem #1:
We’re trying to prove that angle X is equal to angle Z. We’re given that side WX = WZ, and Y is the midpoint of XZ.
Step 1: We already know WX ≅ WZ — that’s given.
Step 2: Y is the midpoint of XZ — also given.
Step 3: Since Y is the midpoint, that means it cuts XZ into two equal parts. So XY = YZ. That’s called the “Definition of midpoint.”
Step 4: If XY = YZ, then those sides are congruent (same length). That’s the “Definition of congruence.”
Step 5: Side WY is in both triangles (WXY and WZY). Any side that’s shared by two triangles is equal to itself. That’s called the “Reflexive Property.”
Step 6: Now we have three pairs of equal sides:
- WX = WZ (given)
- XY = YZ (from midpoint)
- WY = WY (same side)
So, by SSS (Side-Side-Side), the triangles are congruent.
Step 7: If the triangles are congruent, then their matching angles are equal too. So angle X = angle Z. That’s called “CPCTC” — which stands for “Corresponding Parts of Congruent Triangles are Congruent.”
That’s how we fill in all the blanks!
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Parent Tip: Review the logic above to help your child master the concept of proving triangles congruent worksheet.
