Let u = ⟨9, –2⟩, v = ⟨–4, 3⟩, and w = ⟨5, 1⟩. Kelcy incorrectly determined 3u – 5(v + w) to be ⟨32, –26⟩. Review her steps as shown. 3u – 5(v + w)

3⟨9, –2⟩ – 5[⟨–4, 3⟩ + ⟨5, 1⟩]

⟨27, –6⟩ – 5[⟨–1, 4⟩]

⟨27, –6⟩ + ⟨5, –20⟩

⟨32, –26⟩

What mistake did Kelcy make?

Given: abcd is a square. prove: ac ? bd. we are given that abcd is a square. if we consider triangle aeb and triangle aed, we see that side is congruent to side ad because sides of a square are congruent. we know that side ae is congruent to side ae by using the . finally, we know that side de is congruent to side because the diagonals of a square bisect each other. therefore, triangle aeb is congruent to triangle aed by congruency. we see that angle aed and angle aeb are a linear pair, and congruent by cpctc. thus, the measure of these angles will be 90°, and diagonal ac is perpendicular to diagonal bd by the .