MA.912.G.3.3: Use coordinate geometry to prove properties of congruent, regular, and similar quadrilaterals

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Geometry Mini-Lesson
On the coordinate plane at right quadrilateral
PQRS has vertices with integer coordinates.Quadr
ilateral EFGH is congruent to quadrilateral PQRS.
Which of the following could be possible
coordinates for point G?

1. (1, -2)
2. (1, 4)
3. (-2, -4)
4. (-2, -10)

MA.912.G.3.3 Use coordinate geometry to prove
properties of congruent, regular, and similar
quadrilaterals
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Geometry Mini-Lesson
Quadrilateral RSTU, shown at right, has integer
coordinates.Which of the following arguments
correctly answers and justifies the question "Is
quadrilateral RSTU a regular quadrilateral?"

1. Yes, it is a regular quadrilateral because all
   sides are the same length.
2. Yes, it is a regular quadrilateral because the
   diagonals are perpendicular.
3. No, it is not a regular quadrilateral because
   RSTU is not a parallelogram.
4. No, it is not a regular quadrilateral because the
   diagonals are not the same length.

MA.912.G.3.3 Use coordinate geometry to prove
properties of congruent, regular, and similar
quadrilaterals
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Geometry Mini-Lesson
Quadrilateral QRST and quadrilateral WXYZ, shown
at right, both have integer coordinates.Are
quadrilateral QRST and quadrilateral WXYZ similar
quadrilaterals?

1. Yes, both are rectangles.
2. No, although the corresponding angles are
   congruent, the rectangles are not the same size.
3. Yes, corresponding angles are congruent and
   corresponding sides have the same scale factor.
4. No, although the corresponding angles are
   congruent, quadrilateral WXYZ is not a reflection
   of quadrilateral QRST.

MA.912.G.3.3 Use coordinate geometry to prove
properties of congruent, regular, and similar
quadrilaterals
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Geometry Mini-Lesson
Quadrilateral MNOP is similar to quadrilateral
QRST. Which of the following could be possible
coordinates for point R?

1. (0, -6)
2. (0, 0)
3. (2, -6)
4. (5, -6)

MA.912.G.3.3 Use coordinate geometry to prove
properties of congruent, regular, and similar
quadrilaterals
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Geometry Mini-Lesson

• Which of the following is the converse of the
  following statement?"If you are a native of
  Florida, then you were born in Florida."
• If you were born in Florida, then you are a
  native of Florida.
• You are a native of Florida if and only if you
  were born in Florida.
• If you are NOT a native of Florida, then you were
  born in Florida.
• If you were NOT born in Florida, then you are NOT
  a native of Florida.

MA.912.D.6.2 Find the converse, inverse and
contrapositive of a statement.
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Geometry Mini-Lesson

• Which of the following is the inverse of the
  following statement?"If two segments are
  congruent, then the two segments have the same
  length."
• If two segments have the same length, then the
  two segments are congruent.
• If two segments are congruent, then the two
  segments do NOT have the same length.
• If two segments are NOT congruent, then the two
  segments do NOT have the same length.
• If two segments do NOT have the same length, then
  the two segments are NOT congruent.

MA.912.D.6.2 Find the converse, inverse and
contrapositive of a statement.
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Geometry Mini-Lesson

• Which of the following is the contrapositive of
  the following statement?"If an animal is a dog,
  then the animal has four legs."
• If an animal has four legs, then the animal is a
  dog.
• If an animal is a dog, then the animal does NOT
  have four legs.
• If an animal does NOT have four legs, then the
  animal is NOT a dog.
• If an animal is NOT a dog, then the animal does
  NOT have four legs.

MA.912.D.6.2 Find the converse, inverse and
contrapositive of a statement.
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Geometry Mini-Lesson

• Which of the following is the converse of the
  following statement?"If a triangle is
  equilateral, then the triangle is isosceles."
• If a triangle is isosceles, then the triangle is
  equilateral.
• If a triangle is NOT equilateral, then the
  triangle is isosceles.
• If a triangle is isosceles, then the triangle is
  NOT equilateral.
• If a triangle is NOT isosceles, then the triangle
  is NOT equilateral.

MA.912.D.6.2 Find the converse, inverse and
contrapositive of a statement.
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Geometry Mini-Lesson

• Which of the following is the inverse of the
  following statement?"If a triangle is a right
  triangle, then the triangle has one right angle."
  
• If a triangle has one right angle, then the
  triangle is a right triangle.
• If a triangle is NOT a right triangle, then the
  triangle has one right angle.
• If a triangle is NOT a right triangle, then the
  triangle does NOT have one right angle.
• If a triangle does NOT have one right angle, then
  the triangle is NOT a right triangle

MA.912.D.6.2 Find the converse, inverse and
contrapositive of a statement.
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Geometry Mini-Lesson

• Which of the following is the converse of the
  following statement?"If you are a native of
  Tallahassee, then you were born in Tallahassee."
• If you were born in Tallahassee, then you are a
  native of Tallahassee.
• You were born in Tallahassee if and only if you
  are a native of Tallahassee.
• If you are NOT a native of Tallahassee, then you
  were NOT born in Tallahassee.
• If you were NOT born in Tallahassee, then you are
  NOT a native of Tallahassee.

MA.912.D.6.2 Find the converse, inverse and
contrapositive of a statement.
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Geometry Mini-Lesson

• Which of the following is the inverse of the
  following statement?"If two angles are
  congruent, then the two angles have the same
  measure."
• If two angles have the same measure, then the two
  angles are congruent.
• If two angles are congruent, then the two angles
  do NOT have the same measure.
• If two angles are NOT congruent, then the two
  angles do NOT have the same measure.
• If two angles do NOT have the same measure, then
  the two angles are NOT congruent.

MA.912.D.6.2 Find the converse, inverse and
contrapositive of a statement.
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Geometry Mini-Lesson

• Which of the following is the converse of the
  following statement?"If a number ends in 7,
  then the number is odd."
• If a number is odd, then the number ends in 7.
• If a number ends in 7, then the number is NOT
  odd.
• If a number is NOT odd, then the number does NOT
  end in 7.
• If a number does NOT end in 7, then the number is
  NOT odd.

MA.912.D.6.2 Find the converse, inverse and
contrapositive of a statement.
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Geometry Mini-Lesson
Mary is asked to prove that is congruent
to in the figure.
She writes the following proofStep 1 is
congruent to because that information is
given in the figure.Step 2 is perpendicular
to because that information is given in the
figure.Step 3 is congruent to by the
reflexive property.Step 4 ADB and CDB are right
angles because perpendicular lines meet to form
right angles.Step 5 ADB is congruent to CDB
because all right angles are congruent.Step 6
_____________________________Step 7 By CPCTC,
is congruent to .
Which of the following answer choices is correct
for Step 6?

1. ?ABD is congruent to ?CBD by SSS.
2. ?ABD is congruent to ?CBD by SAS.
3. ?ABD is congruent to ?CBD by AAS.
4. ?ABD is congruent to ?CBD by ASA.

MA.912.G.4.6 Prove that triangles are congruent
or similar and use the concept of corresponding
parts of congruent triangles
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Geometry Mini-Lesson
What can you prove to be true about the two
triangles in the diagram provided?

1. ?ABC is similar but not congruent to ?XYZ.
2. ?ABC is similar and congruent to ?XYZ.
3. ?ABC is congruent but not similar to ?XYZ.
4. There is not enough information to conclude any
   relationship between ?ABC and ?XYZ.

MA.912.G.4.6 Prove that triangles are congruent
or similar and use the concept of corresponding
parts of congruent triangles
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Geometry Mini-Lesson
Given the figure, which of the answer choices is
TRUE?

1. ?ABC and ?XYZ are congruent by ASA
2. ?CBA and ?ZYX are congruent by ASA
3. ?CAB and ?ZXY are congruent by AAS
4. ?ABC and ?ZYX are congruent by AAS

MA.912.G.4.6 Prove that triangles are congruent
or similar and use the concept of corresponding
parts of congruent triangles
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Geometry Mini-Lesson
Given the figure, which of the answer choices is
TRUE?

1. ?CBA and ?DEC are congruent by ASA and is
   congruent to by CPCTC.
2. ?ABC and ?DEC are congruent by ASA and is
   congruent to by CPCTC.
3. ?BCA and ?ECD are congruent by AAS and is
   congruent to by CPCTC.
4. ?CAB and ?CDE are congruent by AAS and is
   congruent to by CPCTC.

MA.912.G.4.6 Prove that triangles are congruent
or similar and use the concept of corresponding
parts of congruent triangles
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Geometry Mini-Lesson
MA.912.G.4.6 Prove that triangles are congruent
or similar and use the concept of corresponding
parts of congruent triangles
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Geometry Mini-Lesson
MA.912.G.4.6 Prove that triangles are congruent
or similar and use the concept of corresponding
parts of congruent triangles
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Geometry Mini-Lesson
MA.912.G.4.6 Prove that triangles are congruent
or similar and use the concept of corresponding
parts of congruent triangles
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Geometry Mini-Lesson
MA.912.G.4.6 Prove that triangles are congruent
or similar and use the concept of corresponding
parts of congruent triangles
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Geometry Mini-Lesson
MA.912.G.4.6 Prove that triangles are congruent
or similar and use the concept of corresponding
parts of congruent triangles
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Geometry Mini-Lesson
Tony is drawing a regular polygon. He has drawn
two of the sides with an interior angle of 120,
as shown below.How many sides will the regular
polygon have when Tony completes his drawing?

1. 6
2. 7
3. 8
4. 9

MA.912.G.2.2 Determine the measures of interior
and exterior angles of polygons, justifying the
method used
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Geometry Mini-Lesson
John is drawing a regular polygon. He has drawn
two sides with an exterior angle measure of 45,
as shown. When John completes his regular
polygon, what will be the sum, in degrees, of the
measures of the interior angles?
Gridded Response Correct Answer 1080
MA.912.G.2.2 Determine the measures of interior
and exterior angles of polygons, justifying the
method used
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Geometry Mini-Lesson
Mindy is drawing a regular polygon. She has drawn
two sides with an exterior angle measure of 36,
as shown below.When she completes her regular
polygon, what will be the sum, in degrees, of the
measures of the interior angles?
Gridded Response Correct Answer 1440
MA.912.G.2.2 Determine the measures of interior
and exterior angles of polygons, justifying the
method used
29
Geometry Mini-Lesson
Sonja is drawing a regular polygon. She has drawn
two of the sides with an interior angle of 150,
as shown.How many sides will the regular
polygon have when Sonja completes her drawing?

1. 10
2. 11
3. 12
4. 13

MA.912.G.2.2 Determine the measures of interior
and exterior angles of polygons, justifying the
method used
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Geometry Mini-Lesson
Review the triangle below. What is the measure of
the exterior angle shown?

1. 42
2. 64
3. 117
4. 126

MA.912.G.2.2 Determine the measures of interior
and exterior angles of polygons, justifying the
method used
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Geometry Mini-Lesson
In the pentagon below, what is the measure of the
exterior angle shown?

1. 45
2. 81
3. 99
4. 137

MA.912.G.2.2 Determine the measures of interior
and exterior angles of polygons, justifying the
method used
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Geometry Mini-Lesson
Find the value of x in the pentagon below.

1. 18
2. 18.9
3. 19.6
4. 20

MA.912.G.2.2 Determine the measures of interior
and exterior angles of polygons, justifying the
method used
33
Geometry Mini-Lesson
Find the value of x in the octagon below.

1. 34
2. 36
3. 57
4. 69

MA.912.G.2.2 Determine the measures of interior
and exterior angles of polygons, justifying the
method used
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Geometry Mini-Lesson
A regular pentagon and a regular hexagon share a
vertex, as shown below.What is the value of x,
in degrees?
Gridded Response Correct Answer 13
MA.912.G.2.2 Determine the measures of interior
and exterior angles of polygons, justifying the
method used
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Geometry Mini-Lesson
A regular pentagon shares each of its sides with
an equilateral triangle, as shown.What is the
value of x, in degrees?
Gridded Response Correct Answer 132
MA.912.G.2.2 Determine the measures of interior
and exterior angles of polygons, justifying the
method used
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Geometry Mini-Lesson
An observer standing near a shoreline sees a
ship. Given the measurements shown in the figure,
how far is the ship from the shoreline, to the
nearest meter?

1. 139 meters
2. 150 meters
3. 174 meters
4. 189 meters

MA.912.G.2.3 Use properties of congruent and
similar polygons to solve mathematical or
real-world problems
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Geometry Mini-Lesson
The side length of square ABCD is 1 unit. Its
diagonal, AC, is a side of square ACEF. Square
ACEF is then enlarged by a scale factor of 2.
What is the area of the enlargement, in square
units?

1. 1 square unit
2. 2 square units
3. 4 square units
4. 8 square units

MA.912.G.2.3 Use properties of congruent and
similar polygons to solve mathematical or
real-world problems
39
Geometry Mini-Lesson
Which of the triangles is an equilateral triangle?
A
B
C
D
MA.912.G.2.3 Use properties of congruent and
similar polygons to solve mathematical or
real-world problems
40
Geometry Mini-Lesson

1. 175 m
2. 200 m
3. 262 m
4. 434 m

MA.912.G.2.3 Use properties of congruent and
similar polygons to solve mathematical or
real-world problems
41
Geometry Mini-Lesson
Given ?ABC and DE is parallel to AC, which of the
following is true?
MA.912.G.2.3 Use properties of congruent and
similar polygons to solve mathematical or
real-world problems