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Slope diagram showing quadrilateral ABCD with labeled points and slope calculation

A quadrilateral ABCD is shown. A coordinate grid with x and y axes ranging from negative six to six in increments of one is shown. A quadrilateral ABCD is drawn by joining point A at four, four, point B at six, one, point C at four, negative two, and point D at two, one. What is true about the slopes of the sides of quadrilateral ABCD? The product of the slopes of DC and AB is -1. The slope of DC and the slope of AB are equal. The slope of AD and the slope of AB are equal. The product of the slopes of AD and AB is -1.

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Image of quadrilateral EFGH with labeled vertices and dashed lines representing its sides and diagonals.

The quadrilateral EFGH has vertices E(−3, 2) , F(3, 2) , G(3, −2) , and H(−3, −2) . Which statement is correct? Quadrilateral EFGH is a square. Quadrilateral EFGH is a rectangle. Quadrilateral EFGH is a rhombus Quadrilateral EFGH is a trapezium.

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A parallelogram is shown below. Which angles and sides must be congruent to each other? Select all that apply. MN ≅ NP MN ≅ OP MO ≅ NP ∠M ≅ ∠O ∠N ≅ ∠P ∠M ≅ ∠P

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No image description is needed for this question as it is a purely text-based question.

A square PQRS has vertices P(2, 4) , Q(6, 8) , R(10, 4) and S(6, 0) . Which set of steps should a student follow to prove that the diagonals of the square are perpendicular to each other? Step 1 : Find the slope of diagonal PR (m1) and slope of diagonal QS (m2) . Step 2 : Show that m1=−m2 . Step 1 : Find the slope of diagonal PR (m1) and slope of diagonal QS (m2) . Step 2 : Show that m1+m2=−1 . Step 1 : Find the slope of diagonal PR (m1) and slope of diagonal QS (m2) . Step 2 : Show that m1=m2 . Step 1 : Find the slope of diagonal PR (m1) and slope of diagonal QS (m2) . Step 2 : Show that m1×m2=−1 .

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The equation of the diagonal BD is 2x - 3y + 9 = 0.

ABCD is a square. The equation of the diagonal AC is 3x+2y−7=0 . What is the equation of the diagonal BD , if the coordinates of vertex B are (3, 5) ? 2x+3y+9=0 3x+2y−7=0 3x−2y−3=0 2x−3y+9=0

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The image accompanying this question could be a diagram of parallelogram RSTU, with labeled sides and angles, highlighting the congruent sides RS¯¯¯¯¯≅TU¯¯¯¯¯ and RU¯¯¯¯¯≅TS¯¯¯¯¯.

Parallelogram RSTU is shown below. Ilan needs to prove that RS¯¯¯¯¯≅TU¯¯¯¯¯ and RU¯¯¯¯¯≅TS¯¯¯¯¯ . His proof is shown in the table below. Step Statement 1 RSTU is a parallelogram 2 RS¯¯¯¯¯ is parallel to TU¯¯¯¯¯ and RU¯¯¯¯¯ is parallel to TS¯¯¯¯¯ 3 ∠RSU≅∠TUS and ∠RUS≅∠TSU 4 SU¯¯¯¯¯≅US¯¯¯¯¯ 5 △RSU≅△TUS 6 RS¯¯¯¯¯≅TU¯¯¯¯¯ and RU¯¯¯¯¯≅TS¯¯¯¯¯ Select ALL reasons that support one or more statements in the proof. symmetric property definition of a parallelogram alternate interior angles are congruent opposite sides of a parallelogram are congruent corresponding parts of congruent triangles are congruent

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The image related to the question would be a diagram showcasing the parallelogram RSTU with labeled sides and angles, along with the steps of the proof in a table format.

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