Geometry: Unit 3 Congruence Test Fields

Last updated about 2 hours ago

25 Nsɛmmisa

Laabri

Geometry: Unit 3 Congruence Test Fields

Last updated about 2 hours ago

25 Nsɛmmisa

Use the answer choices to fill-in each of the blanks to correctly classify the type of triangle by its angle and sides.

1

Given $ \triangle PQR \cong \triangle XYZ $, which statement is true?

1

Identify the Rigid Transformation

Identify the rigid transformation that can be used to map each figure onto each other to prove that they are congruent.

1

Translation

Rotation

Reflection

1

Determine if it is possible to prove that each pair of triangles are congruent or are not necessarily congruent. If it is possible to prove that the triangles are congruent, choose the congruence postulate or theorem that you would use in your proof.

1

Geometric proof with a diagram showing triangle WXY with right angle at Z and equal sides marked.

Given: $WX \perp YZ, \, WY \cong XY$

Prove: Base angles of the isosceles $\triangle WXY$ are congruent.

Match each blank in the proof with the correct statement:

Statements	Reasons
$YZ \, \|\| \, WX$	Given
$WY \cong XY$	Given
1)	Reflexive Property ($\cong$ to itself)
2)	Hypotenuse-Leg Theorem
3)	Corresponding Parts of $\cong$ Triangles are $\cong$

1

1) _________________

1

2) _________________

1

3) _________________

1

What is the value of $x$ and what is the length of each side of the equilateral triangle?
Complete each of the following 2 activities (A - B) for Question 11.
You may find it very helpful to refer back to previous parts of this task.
What is the value of $x$ in the equilateral triangle?
You may find it very helpful to refer back to previous parts of this task.
What is the length of each side of the equilateral triangle?

1

What is the measure of $\angle B$?

The triangular faces of the peaks on a roof are congruent isosceles triangles with vertex angles $U$ and $V$.

Diagram of a roof with two triangular sections labeled with points U, V, W, X, and Y. The width between W and X is 8 meters, and the height from W to U is 6.5 meters.

Complete each of the following 2 activities (A - B) for Question 13.

You may find it helpful to return to previous parts of this task. Match each angle with names of other congruent angles.

1

You may find it helpful to return to previous parts of this task. What is the distance in meters between points $U$ and $V$?

1

Given $ \triangle PQR \cong \triangle XYZ $, which statement is true?

1

Identify the transformation that results in the shape and/or size of the figure being distorted.

Dilation

Horizontal Stretch

Vertical Stretch

Identify the Rigid Transformation

Identify the rigid transformation that can be used to map each figure onto each other to prove that they are congruent.

1

Translation

Rotation

Reflection

1

Translation

Rotation

Reflection

1

Translation

Rotation

Reflection

Geometric proof with a diagram showing triangle WXY with right angle at Z and equal sides marked.

Given: $WX \perp YZ, \, WY \cong XY$

Prove: Base angles of the isosceles $\triangle WXY$ are congruent.

Match each blank in the proof with the correct statement:

Statements	Reasons
$YZ \, \|\| \, WX$	Given
$WY \cong XY$	Given
1)	Reflexive Property ($\cong$ to itself)
2)	Hypotenuse-Leg Theorem
3)	Corresponding Parts of $\cong$ Triangles are $\cong$

1

1) _________________

1

2) _________________

1

3) _________________

Answer Choices

A. $YZ \cong YZ$
B. $WZ \cong XZ$
C. $\triangle WYZ \cong \triangle XZY$
D. $\triangle WZY \cong \triangle XZY$
E. $\angle WYZ \cong \angle XYZ$
F. $\angle YWZ \cong \angle YXZ$

1

Given: $m \angle PQR = m \angle TSR = 90^\circ$, $PQ \equiv TS$
Prove: $PR \equiv TR$
Match each blank in the proof with the correct reasoning:
Statements
Reasons
$m \angle PQR = m \angle TSR = 90^\circ$
Given
$PQ \equiv TS$
Given
$\angle PRQ \equiv \angle SRT$
1)
$\triangle PRQ \equiv \triangle SRT$
2)
$PR \equiv TR$
3)
Questions
1)
2)
3)
Answer Choices
Angle-Angle-Side Postulate
Corresp. Parts of $\cong \triangle$ are $\cong$
Hypotenuse-Leg Theorem
Side-Side-Angle Postulate
Reflexive Property ($\cong$ to itself)
Vertical Angles

1

Which theorem or postulate can be used to prove the triangles are congruent given that $AB \parallel CD$ and $\angle ACB \equiv \angle DBC$ and what congruence statement relates the given triangles?
Complete each of the following 2 activities (A - B) for Question 9.

A

B

C

D

1

What is the value of $x$ and what is the length of each side of the equilateral triangle?
Complete each of the following 2 activities (A - B) for Question 11.
You may find it very helpful to refer back to previous parts of this task.
What is the value of $x$ in the equilateral triangle?
You may find it very helpful to refer back to previous parts of this task.
What is the length of each side of the equilateral triangle?

1

What is the measure of $\angle B$?

1. $\triangle HJK$ is a ___________.

2. A triangle with no equal sides and angle measures of 90°, 55° and 35° is a __________.

3. A triangle with angle measures of 30°, 120°, and 30° is a ______________.

What is the measure of $\angle XYZ$?

Identify the transformation that results in the shape and/or size of the figure being distorted.

Dilation

Horizontal Stretch

Vertical Stretch

Translation

Rotation

Reflection

Translation

Rotation

Reflection