7.3.2 Review & Preview

Tomika remembers that the diagonals of a rhombus are perpendicular to each other. 7-131 HW eTool (Desmos). Homework Help

1

Graph ABCD if A(1,4), B(6,6), C(4,1), and D(−1,−1). Is ABCD a rhombus? Show how you know in the work section.

1

Find the equations of the lines on which the diagonals lie. That is, find the equation of AC.

1

Find the equation of BD.

1

Compare the slopes of AC and BD. What do you notice?

1

Find another valid, logical order for the statements for Penn’s proof from problem 7-113 below. Explain how you know that changing the order the way you did does not affect the logic. Homework Help

Each of these number lines shows a segment in bold. Find the midpoint of the segment in bold. Note that the diagrams are not drawn to scale.  Homework Help

1

Examine the diagram at right.  Homework Help

1

Are the triangles in this diagram similar? If they are, use a two-column proof to prove similarity. If they are not similar, explain why not. Explain.

1

Name all the pairs of congruent angles in this diagram you can.

1

Are GH and IJ parallel? Explain how you know.

1

If GH=4x−3 and IJ=3x+14, find x. Then find the length of GH.

Consider ΔABC with vertices A(2,3), B(6,6), and C(8,−5).  7-135 HW eTool (Desmos) Homework Help

1

Draw ΔABC on graph paper. What kind of triangle is ΔABC? Prove your result in the work section.

1

Reflect ΔABC across AC. Find the location of B′. What name best describes the resulting figure? Prove your claim in the work section.

This problem is a checkpoint for solving with trigonometric ratios and the Pythagorean Theorem. It will be referred to as Checkpoint 7. Homework Help

1

Compute the perimeter.

1

Solve for x.

1

Solve for x.

1

Juanito is flying a kite at the park and realizes that all 500 feet of string are out. Margie measures the angle of the string with the ground using her clinometer and finds it to be 42°. How high is Juanito’s kite above the ground? Draw a diagram and use the appropriate trigonometric ratio.

MUST BE, COULD BE
Here are some more challenges from Mr. Quincey. For each description of a quadrilateral below, say what special type the quadrilateral must be and/or what special type the quadrilateral could be. Look out: Some descriptions may have no must be statements, and some descriptions may have many could be statements!  Homework Help

1

My quadrilateral has a pair of equal sides and a pair of parallel sides.

Must be:

1

Could be:

1

The diagonals of my quadrilateral bisect each other.

Must be:

1

7.3.2 Review & Preview

Graph ABCD if A(1,4), B(6,6), C(4,1), and D(−1,−1). Is ABCD a rhombus? Show how you know in the work section.

Find the equations of the lines on which the diagonals lie. That is, find the equation of AC.

Find the equation of BD.

Compare the slopes of AC and BD. What do you notice?

Find another valid, logical order for the statements for Penn’s proof from problem 7-113 below. Explain how you know that changing the order the way you did does not affect the logic. Homework Help

Are the triangles in this diagram similar? If they are, use a two-column proof to prove similarity. If they are not similar, explain why not. Explain.

Name all the pairs of congruent angles in this diagram you can.

Are GH and IJ parallel? Explain how you know.

If GH=4x−3 and IJ=3x+14, find x. Then find the length of GH.

Draw ΔABC on graph paper. What kind of triangle is ΔABC? Prove your result in the work section.

Reflect ΔABC across AC. Find the location of B′. What name best describes the resulting figure? Prove your claim in the work section.

Compute the perimeter.

Solve for x.

Solve for x.

Juanito is flying a kite at the park and realizes that all 500 feet of string are out. Margie measures the angle of the string with the ground using her clinometer and finds it to be 42°. How high is Juanito’s kite above the ground? Draw a diagram and use the appropriate trigonometric ratio.

My quadrilateral has a pair of equal sides and a pair of parallel sides.Must be:

Could be:

The diagonals of my quadrilateral bisect each other.Must be:

Could be:

Graph ABCD if A(1,4), B(6,6), C(4,1), and D(−1,−1). Is ABCD a rhombus? Show how you know in the work section.

Find the equations of the lines on which the diagonals lie. That is, find the equation of AC.

Find the equation of BD.

Compare the slopes of AC and BD. What do you notice?

Find another valid, logical order for the statements for Penn’s proof from problem 7-113 below. Explain how you know that changing the order the way you did does not affect the logic. Homework Help

Are the triangles in this diagram similar? If they are, use a two-column proof to prove similarity. If they are not similar, explain why not. Explain.

Name all the pairs of congruent angles in this diagram you can.

Are GH and IJ parallel? Explain how you know.

If GH=4x−3 and IJ=3x+14, find x. Then find the length of GH.

Draw ΔABC on graph paper. What kind of triangle is ΔABC? Prove your result in the work section.

Reflect ΔABC across AC. Find the location of B′. What name best describes the resulting figure? Prove your claim in the work section.

Compute the perimeter.

Solve for x.

Solve for x.

Juanito is flying a kite at the park and realizes that all 500 feet of string are out. Margie measures the angle of the string with the ground using her clinometer and finds it to be 42°. How high is Juanito’s kite above the ground? Draw a diagram and use the appropriate trigonometric ratio.

My quadrilateral has a pair of equal sides and a pair of parallel sides.Must be:

Could be:

The diagonals of my quadrilateral bisect each other.Must be:

Could be:

My quadrilateral has a pair of equal sides and a pair of parallel sides.

Must be:

The diagonals of my quadrilateral bisect each other.

Must be:

My quadrilateral has a pair of equal sides and a pair of parallel sides.

Must be:

The diagonals of my quadrilateral bisect each other.

Must be: