Figure ABCD is a square. Prove BD ≅ AC. Statements Reasons 1. ABCD is a square 1. given 2. ∠DAB, ∠ABC, ∠BCD, and ∠CDA are right angles 2. definition of a square 3. ∠DAB ≅ ∠ABC ≅ ∠BCD ≅ ∠CDA 3. right angles are congruent 4. AB ≅ BC ≅ CD ≅ DA 4. ? 5. △BAD ≅ △ABC 5. SAS 6. BD ≅ AC 6. CPCTC What is the missing reason in the proof? all sides of a square are congruent all right angles measure 90° definition of diagonal definition of perpendicular

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In case of a square all the sides are congruent . It makes the two diagonals congruent(BD ≅ AC).

What is a square?

"A square is a regular quadrilateral, which means that it has four equal sides and four equal angles( right-angles). It can also be defined as a rectangle with two equal-length adjacent sides."

Here, all the sides of a square is congruent.

Therefore, AB ≅ BC ≅ CD ≅ DA

Hence,  BD ≅ AC

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