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MA.912.G.3.4: Prove theorems involving quadrilaterals.

Geometry Mini-Lesson. Given quadrilateral ABCD , which of the following sufficiently indicates that the quadrilateral is a rectangle?. AB || DC and AD || BC AB is congruent to DC, and AD is congruent to BC A and C are right angles

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MA.912.G.3.4: Prove theorems involving quadrilaterals.

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  1. Geometry Mini-Lesson Given quadrilateral ABCD, which of the following sufficiently indicates that the quadrilateral is a rectangle? • AB || DC and AD || BC • AB is congruent to DC, andAD is congruent to BC • A and C are right angles • AB is congruent to DC, and AB || DC, and B is a right angle MA.912.G.3.4: Prove theorems involving quadrilaterals.

  2. Geometry Mini-Lesson Which statement is FALSE? • Every square is a rhombus. • All rectangles are parallelograms. • The diagonals of all parallelograms bisect each other. • Every property of a square is also a property of a parallelogram. MA.912.G.3.4: Prove theorems involving quadrilaterals.

  3. Geometry Mini-Lesson Figure JKLM is a rhombus. The measure of angle JKM is (2x + 17)° and the measure of angle LKM is (3x − 19)°.Which statement best explains why the equation 2x + 17 = 3x − 19 can be used to find x? • All sides of a rhombus are congruent. • Opposite angles in a rhombus are congruent. • The diagonals of a rhombus are perpendicular. • The diagonals of a rhombus bisect opposite angles. MA.912.G.3.4: Prove theorems involving quadrilaterals.

  4. Geometry Mini-Lesson Jasmine is about to buy a rectangular plot of land to build her house. Before she buys it, she wants to verify the shape is truly rectangular. Which of the following methods should she use to prove the plot of land is a rectangle? • Verify that the diagonals of the plot of land are congruent. • Verify that opposite sides of the plot of land are congruent. • Verify that the diagonals of the plot of land bisect each other. • Verify that consecutive angles of the plot of land are supplementary. MA.912.G.3.4: Prove theorems involving quadrilaterals.

  5. Geometry Mini-Lesson Given a rhombus, which statement is FALSE? • The diagonals are perpendicular. • The diagonals bisect each other. • Exactly one pair of opposite sides is parallel. • Both pairs of opposite angles are congruent. MA.912.G.3.4: Prove theorems involving quadrilaterals.

  6. Geometry Mini-Lesson Figure STUV is a parallelogram. The measure of angle S is (5x + 13)° and the measure of angle T is (7x − 40)°.Which statement best explains why the equation 5x + 13 + 7x − 40 = 180 can be used to find x? • Opposite sides of a parallelogram are parallel. • Opposite angles in a parallelogram are congruent. • Consecutive angles in a parallelogram are supplementary. • Consecutive angles in a parallelogram are complementary. MA.912.G.3.4: Prove theorems involving quadrilaterals.

  7. Geometry Mini-Lesson MA.912.G.3.4: Prove theorems involving quadrilaterals.

  8. Geometry Mini-Lesson • Miguel thinks the shape of his math classroom is a square. Tom disagrees. He thinks the classroom is rectangular but not square. Which of the following methods should Miguel use to prove his rectangular math classroom is truly square? • Verify the diagonals of the classroom are perpendicular. • Verify that opposite sides in the classroom are congruent. • Verify that the diagonals of the classroom are congruent. • Verify that the diagonals of the classroom bisect each other. MA.912.G.3.4: Prove theorems involving quadrilaterals.

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