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

1
(No Transcript)
2
Geometry Mini-Lesson
Given quadrilateral ABCD, which of the following
sufficiently indicates that the quadrilateral is
a rectangle?

1. AB DC and AD BC
2. AB is congruent to DC, andAD is congruent to BC
3. A and C are right angles
4. AB is congruent to DC, and AB DC, and B is a
   right angle

MA.912.G.3.4 Prove theorems involving
quadrilaterals.
3
Geometry Mini-Lesson
Which statement is FALSE?

1. Every square is a rhombus.
2. All rectangles are parallelograms.
3. The diagonals of all parallelograms bisect each
   other.
4. Every property of a square is also a property of
   a parallelogram.

MA.912.G.3.4 Prove theorems involving
quadrilaterals.
4
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?

1. All sides of a rhombus are congruent.
2. Opposite angles in a rhombus are congruent.
3. The diagonals of a rhombus are perpendicular.
4. The diagonals of a rhombus bisect opposite angles.

MA.912.G.3.4 Prove theorems involving
quadrilaterals.
5
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?

1. Verify that the diagonals of the plot of land are
   congruent.
2. Verify that opposite sides of the plot of land
   are congruent.
3. Verify that the diagonals of the plot of land
   bisect each other.
4. Verify that consecutive angles of the plot of
   land are supplementary.

MA.912.G.3.4 Prove theorems involving
quadrilaterals.
6
Geometry Mini-Lesson
Given a rhombus, which statement is FALSE?

1. The diagonals are perpendicular.
2. The diagonals bisect each other.
3. Exactly one pair of opposite sides is parallel.
4. Both pairs of opposite angles are congruent.

MA.912.G.3.4 Prove theorems involving
quadrilaterals.
7
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?

1. Opposite sides of a parallelogram are parallel.
2. Opposite angles in a parallelogram are congruent.
   
3. Consecutive angles in a parallelogram are
   supplementary.
4. Consecutive angles in a parallelogram are
   complementary.

MA.912.G.3.4 Prove theorems involving
quadrilaterals.
8
Geometry Mini-Lesson
MA.912.G.3.4 Prove theorems involving
quadrilaterals.
9
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.