Question 1

Solve.
-Explain how to construct a parallelogram given two adjacent sides. If it is not possible, explain why.

Accepted Answer

The answer of Solve.
-Explain how to construct a parallelogram given...

Question 2

Solve.
-Draw two parallelograms such that two angles and an included side are congruent respectively to two angles and an included side of the other parallelogram, and yet the two parallelograms are not congruent.

Accepted Answer

The answer of Solve.
-Draw two parallelograms such that two angles...

Question 3

Solve.
-Given two 15-cm sides and two 10-cm sides, how many quadrilaterals can be formed with a 75° angle?

Accepted Answer

The answer of Solve.
-Given two 15-cm sides and two 10-cm...

Question 4

Solve.
-How many different rotational symmetries does a square have?
A)5
B)3
C)4
D)2

Accepted Answer

The answer of Solve.
-How many different rotational symmetries does a...

Question 5

Answer the question.
-What type of figure is formed by joining the midpoints of the adjacent sides of a rectangle?

Accepted Answer

The answer of Answer the question.
-What type of figure is...

Question 6

Provide an appropriate response.
-The two triangles shown below are congruent. The sides corresponding to $\overline { \mathrm { AB } } , \overline { \mathrm { BC } }$, and $\overline { \mathrm { AC } }$ (in order) are____

A) $\overline { \mathrm { LN } } , \overline { \mathrm { MN } }$, and $\overline { \mathrm { ML } }$
B) $\overline { \mathrm { ML } } , \overline { \mathrm { LN } }$, and $\overline { \mathrm { MN } }$
C) $\overline { \mathrm { MN } } , \overline { \mathrm { LN } }$, and $\overline { \mathrm { ML } }$
D) $\overline { \mathrm { ML } } , \overline { \mathrm { MN } }$, and $\overline { \mathrm { LN } }$

Accepted Answer

The answer of Provide an appropriate response.
-The two triangles shown...

Question 7

Solve.
-Explain how to construct a parallelogram with exactly three right angles. If it is not possible, explain why.

Accepted Answer

The answer of Solve.
-Explain how to construct a parallelogram with...

Question 8

Solve.
-Can a quadrilateral be formed given two 10-cm sides and a 75° angle that is not a trapezoid, parallelogram, kite, or rhombus?

Accepted Answer

The answer of Solve.
-Can a quadrilateral be formed given two...

Question 9

Provide an appropriate response.
-The two triangles shown below are congruent. $\triangle \mathrm { ABC } \cong$______

A) $\triangle W Z X$
B) $\triangle X Z W$
C) $\triangle X W Z$
D) $\triangle W X Z$

Accepted Answer

The answer of Provide an appropriate response.
-The two triangles shown...

Question 10

Provide an appropriate response.
-The two triangles shown below are congruent. The angles corresponding to $\angle E , \angle F$, and $\angle G$ (in order) are____ 
A) $\angle M , \angle K$, and $\angle L$
B) $L , \angle K$, and $\angle M$
C) $\angle \mathrm { K } , \angle$, and $\angle \mathrm { M }$
D) $\angle K , \angle M$, and $\angle L$

Accepted Answer

The answer of Provide an appropriate response.
-The two triangles shown...

Question 11

Provide an appropriate response.
-The two triangles shown below are congruent. The vertices corresponding to A, B, and C (in order) are .

A) X , Y and Z
B) Y, X and Z
C) Y , Z and X 
D) Z, X and Y

Accepted Answer

The answer of Provide an appropriate response.
-The two triangles shown...

Question 12

Solve.
-Explain how to construct a line parallel to a line l using the sliding-triangle method.

Accepted Answer

The answer of Solve.
-Explain how to construct a line parallel...

Question 13

Solve.
-Explain how to construct a square given one side $\overline { \mathrm { AB } }$ and constructing only parallel lines. If it is not possible, explain why.

Accepted Answer

The answer of Solve.
-Explain how to construct a square given...

Question 14

Provide an appropriate response.
-The two triangles shown below are congruent. The angles corresponding to $\angle , \angle K$, and $\angle$ (in order) are____

A) $\angle S , \angle Q$, and $\angle R$
B) $S S , \angle R$, and $\angle Q$
C) $\angle Q , \angle R$, and $\angle S$
D) $\angle R , \triangle S$, and $\angle Q$

Accepted Answer

The answer of Provide an appropriate response.
-The two triangles shown...

Question 15

Solve.
-Consider the isosceles triangles ABC and PQR. If side AB is glued to side PQ, what type of quadrilateral is formed?

Accepted Answer

The answer of Solve.
-Consider the isosceles triangles ABC and PQR....

Question 16

Provide an appropriate response.
-The two triangles shown below are congruent. $\triangle \mathrm { IJK } \cong$_____

A) $\triangle \mathrm { NLM }$
B) $\triangle \mathrm { NML }$
C) $\triangle \mathrm { MNL }$
D) $\triangle \mathrm { LMN }$

Accepted Answer

The answer of Provide an appropriate response.
-The two triangles shown...

Question 17

Solve.
-Consider the two congruent equilateral triangles ABC and PQR. If side AB is glued to side PQ, what type of quadrilateral is formed?

Accepted Answer

The answer of Solve.
-Consider the two congruent equilateral triangles ABC...

Question 18

Answer the question.
-John goes to a building and stands 100 feet away. He measures the angle of elevation to the top of the building as 37°. He also measures the angle of elevation 100 feet away from a different building. It is the same. He concludes that the buildings are the same height. Is he right? Explain.

Accepted Answer

The answer of Answer the question.
-John goes to a building...

Question 19

Provide an appropriate response.
-The two triangles shown below are congruent. The vertices corresponding to H, I, and J (in order) are . 
A) $\mathrm { L } , \mathrm { K }$, and $\mathrm { M }$
B) $\mathrm { K } , \mathrm { M }$, and $\mathrm { L }$
C) $\mathrm { M } , \mathrm { K }$, and $\mathrm { L }$
D) $\mathrm { K } , \mathrm { L }$, and $\mathrm { M }$

Accepted Answer

The answer of Provide an appropriate response.
-The two triangles shown...

Question 20

Answer the question.
-Joe is building a deck. He nails a 10-foot, 2" by 8" board along the back of the house. He intends to use two 8-foot boards for the sides out to the corner posts. Then he will use another 10-foot board for the end. How can Joe make sure his deck is a rectangle, not a parallelogram, without checking the angles formed at the corners?

Accepted Answer

The answer of Answer the question.
-Joe is building a deck....

Quiz 12: Congruence and Similarity With Constructions

Solve. -Explain how to construct a parallelogram given two adjacent sides. If it is not possible, explain why.

Solve. -Draw two parallelograms such that two angles and an included side are congruent respectively to two angles and an included side of the other parallelogram, and yet the two parallelograms are not congruent.

Solve. -Given two 15-cm sides and two 10-cm sides, how many quadrilaterals can be formed with a 75° angle?

Solve. -How many different rotational symmetries does a square have?

Answer the question. -What type of figure is formed by joining the midpoints of the adjacent sides of a rectangle?

Provide an appropriate response. -The two triangles shown below are congruent. The sides corresponding to AB‾,BC‾\overline { \mathrm { AB } } , \overline { \mathrm { BC } }AB,BC , and AC‾\overline { \mathrm { AC } }AC (in order) are____

Solve. -Explain how to construct a parallelogram with exactly three right angles. If it is not possible, explain why.

Solve. -Can a quadrilateral be formed given two 10-cm sides and a 75° angle that is not a trapezoid, parallelogram, kite, or rhombus?

Provide an appropriate response. -The two triangles shown below are congruent. △ABC≅\triangle \mathrm { ABC } \cong△ABC≅ ______

Provide an appropriate response. -The two triangles shown below are congruent. The angles corresponding to ∠E,∠F\angle E , \angle F∠E,∠F , and ∠G\angle G∠G (in order) are____

Provide an appropriate response. -The two triangles shown below are congruent. The vertices corresponding to A, B, and C (in order) are .

Solve. -Explain how to construct a line parallel to a line l using the sliding-triangle method.

Solve. -Explain how to construct a square given one side AB‾\overline { \mathrm { AB } }AB and constructing only parallel lines. If it is not possible, explain why.

Provide an appropriate response. -The two triangles shown below are congruent. The angles corresponding to ∠,∠K\angle , \angle K∠,∠K , and ∠\angle∠ (in order) are____

Solve. -Consider the isosceles triangles ABC and PQR. If side AB is glued to side PQ, what type of quadrilateral is formed?

Provide an appropriate response. -The two triangles shown below are congruent. △IJK≅\triangle \mathrm { IJK } \cong△IJK≅ _____

Solve. -Consider the two congruent equilateral triangles ABC and PQR. If side AB is glued to side PQ, what type of quadrilateral is formed?

Provide an appropriate response. -The two triangles shown below are congruent. The vertices corresponding to H, I, and J (in order) are .

Solve. -Explain how to construct a square given one side $\overline { \mathrm { AB } }$ and constructing only parallel lines. If it is not possible, explain why.