Triangle Congruence and Properties Quiz

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What can be concluded if ∆XYZ is congruent to ∆MNL?

Side YZ is equal to side UL.

Angle Z is larger than angle N.

Angle Y is equal to angle M. (correct)

Side XY is longer than side MN.

If a triangle has angles measuring 35°, 45°, and 100° it can be considered congruent to another triangle with angles measuring 35°, 45°, and 100°.

True

What is the measure of angle B in the quadrilateral ABCD if angle D is 28° and angle B is 135°?

135°

In quadrilateral ABCD, if angle B is 135° and angle D is 28°, then angle F, which is equal to angle B, must measure ___°.

135 Signup and view all the answers

Match the following angles with their corresponding triangle in the congruence problems:

Angle Y = Angle M Angle Z = Angle L Angle N = Angle U Angle M = Angle T Signup and view all the answers

What theorem would you most likely use to demonstrate that two triangles are congruent given that two sides and the included angle of one triangle are equal to the corresponding parts of another triangle?

SAS (Side-Angle-Side) Theorem Signup and view all the answers

An equilateral triangle has all angles measuring 60 degrees.

True Signup and view all the answers

What are the properties of an isosceles triangle?

An isosceles triangle has at least two sides that are equal in length and the angles opposite those sides are also equal. Signup and view all the answers

In a triangle with congruent sides, the angles opposite these sides are __________.

congruent Signup and view all the answers

Match the following types of triangles with their characteristics:

Equilateral Triangle = All sides and angles are equal Isosceles Triangle = At least two sides are equal Scalene Triangle = All sides and angles are different Right Triangle = One angle measures exactly 90 degrees Signup and view all the answers

Which of the following postulates can be used to determine triangle congruence with two sides and the included angle?

SAS Signup and view all the answers

AAS can be used to prove triangle congruence if two angles and a non-included side are known.

True Signup and view all the answers

What additional information is needed to prove that two triangles are congruent using the SSS postulate?

The lengths of all three sides of both triangles. Signup and view all the answers

The postulate used when two angles and the included side are known is called __________.

ASA Signup and view all the answers

Match the following congruence postulates with their descriptions:

SSS = Three sides are equal SAS = Two sides and the included angle are equal ASA = Two angles and the included side are equal AAS = Two angles and a non-included side are equal Signup and view all the answers

In a triangle with angle measures of 52°, x°, and an implied 76°, what is the value of x?

28° Signup and view all the answers

In a triangle, if two angles are known as 43° and x°, then the third angle can be found by subtracting the sum of these angles from 180°.

True Signup and view all the answers

What is the relationship among the angles in any triangle?

The sum of the angles is always 180°. Signup and view all the answers

In a triangle, if one angle is x° and the other angle is 90°, the third angle can be expressed as __________.

90 - x Signup and view all the answers

Match the triangle problem with its solution method:

Problem 1 = Use the triangle angle sum property Problem 2 = Set up an equation with common angles Problem 3 = Utilize exterior angle theorem Problem 4 = Use corresponding angles in similar triangles Signup and view all the answers

Which property confirms that if $ riangle QRS riangle TUV$ and $ riangle TUV riangle XYZ$, then $ riangle QRS riangle XYZ$?

Transitive property Signup and view all the answers

$ riangle EFG riangle JKL$ implies $ riangle JKL riangle EFG$.

True Signup and view all the answers

What is the measure of angle L?

70 degrees Signup and view all the answers

If $AB riangle DC$ and $E$ is the midpoint of $AC$, then you can prove that $ riangle AEB riangle CED$.

congruent Signup and view all the answers

What is needed to prove $ riangle BAEG riangle DEGC$?

One additional congruency condition Signup and view all the answers

Match the congruence properties to their definitions:

Transitive property = If A = B and B = C, then A = C Symmetric property = If A = B, then B = A Reflexive property = A = A Signup and view all the answers

The corresponding parts of congruent triangles are congruent.

True Signup and view all the answers

What happens to the y-coordinates of points when reflected across the x-axis?

They are negated. Signup and view all the answers

What is the reason for the statement $ riangle COS ext{ is congruent to } riangle WOS$ in Problem 3?

Angle-Side-Angle (ASA) Congruence. Signup and view all the answers

How can you determine the measure of angle GBE?

By recognizing corresponding angles in the congruent triangles. Signup and view all the answers

Reflection across the line y=x involves swapping x and y coordinates.

True Signup and view all the answers

In Problem 4, both $ riangle FRS$ and $ riangle GOS$ are right triangles.

True Signup and view all the answers

If a point is located at (3, -4), what will be its coordinates after reflecting across the line y=-2?

(3, 0) Signup and view all the answers

When reflecting a point across the line x=-1, the distance from the point to the line is kept the same but moved to the ______ side.

opposite Signup and view all the answers

What properties are used to prove that $ riangle COS ext{ is congruent to } riangle WOS$?

Angle Bisector Theorem, Reflexive Property Signup and view all the answers

In Problem 4, angles R and G are both classified as ______.

right angles Signup and view all the answers

Match each reflection line with its characteristic:

x-axis = Negates y-coordinates y=-2 = Maintains distance from the line y=x = Swaps x and y coordinates x=-1 = Maintains distance from the line Signup and view all the answers

Match the following triangles with their characteristics based on the problems presented:

$ riangle COS$ = Congruent to $ riangle WOS$ $ riangle FRS$ = Contains a right angle at R $ riangle GOS$ = Contains a right angle at G $ riangle WOS$ = Has a corresponding angle $ riangle COS$ Signup and view all the answers

What can be concluded about segments DE and CE in the first proof?

DE = CE Signup and view all the answers

The statement '∠ANY ≅ ∠YDA' can be proven without establishing a relationship between angles and segments first.

False Signup and view all the answers

List the given information for the second proof.

DA || YN, DA ≅ YN Signup and view all the answers

In the first proof, the definition of segment bisectors indicates that _______.

DE = CE Signup and view all the answers

Match the following statements to their roles in the proofs:

CD bisects AB = Given DA || YN = Given DE = CE = Definition of segment bisectors DA ≅ YN = Given Signup and view all the answers

Which of the following best describes a transformation where a figure is slid to a new location without changing its shape or size?

Translation Signup and view all the answers

A reflection transformation results in a figure that is identical to the original figure except for its orientation.

True Signup and view all the answers

What is the formula for a translation of a geometric figure in the coordinate plane?

T(x,y) = (x+a, y+b) Signup and view all the answers

A ________ transformation enlarges or reduces a figure but keeps its shape.

dilation Signup and view all the answers

Match the type of transformation to its correct description:

Translation = Moving the figure without changing its size or shape Rotation = Turning the figure around a fixed point Reflection = Flipping the figure over a line Dilation = Resizing the figure while keeping the shape constant Signup and view all the answers

Triangle Congruence and Properties Quiz

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Questions and Answers

What can be concluded if ∆XYZ is congruent to ∆MNL?

If a triangle has angles measuring 35°, 45°, and 100° it can be considered congruent to another triangle with angles measuring 35°, 45°, and 100°.

What is the measure of angle B in the quadrilateral ABCD if angle D is 28° and angle B is 135°?

In quadrilateral ABCD, if angle B is 135° and angle D is 28°, then angle F, which is equal to angle B, must measure ___°.

Match the following angles with their corresponding triangle in the congruence problems:

What theorem would you most likely use to demonstrate that two triangles are congruent given that two sides and the included angle of one triangle are equal to the corresponding parts of another triangle?

An equilateral triangle has all angles measuring 60 degrees.

What are the properties of an isosceles triangle?

In a triangle with congruent sides, the angles opposite these sides are __________.

Match the following types of triangles with their characteristics:

Which of the following postulates can be used to determine triangle congruence with two sides and the included angle?

AAS can be used to prove triangle congruence if two angles and a non-included side are known.

What additional information is needed to prove that two triangles are congruent using the SSS postulate?

The postulate used when two angles and the included side are known is called __________.

Match the following congruence postulates with their descriptions:

In a triangle with angle measures of 52°, x°, and an implied 76°, what is the value of x?

In a triangle, if two angles are known as 43° and x°, then the third angle can be found by subtracting the sum of these angles from 180°.

What is the relationship among the angles in any triangle?

In a triangle, if one angle is x° and the other angle is 90°, the third angle can be expressed as __________.

Match the triangle problem with its solution method:

Which property confirms that if $ riangle QRS riangle TUV$ and $ riangle TUV riangle XYZ$, then $ riangle QRS riangle XYZ$?

$ riangle EFG riangle JKL$ implies $ riangle JKL riangle EFG$.

What is the measure of angle L?

If $AB riangle DC$ and $E$ is the midpoint of $AC$, then you can prove that $ riangle AEB riangle CED$.

What is needed to prove $ riangle BAEG riangle DEGC$?

Match the congruence properties to their definitions:

The corresponding parts of congruent triangles are congruent.

What happens to the y-coordinates of points when reflected across the x-axis?

What is the reason for the statement $ riangle COS ext{ is congruent to } riangle WOS$ in Problem 3?

How can you determine the measure of angle GBE?

Reflection across the line y=x involves swapping x and y coordinates.

In Problem 4, both $ riangle FRS$ and $ riangle GOS$ are right triangles.

If a point is located at (3, -4), what will be its coordinates after reflecting across the line y=-2?

When reflecting a point across the line x=-1, the distance from the point to the line is kept the same but moved to the ______ side.

What properties are used to prove that $ riangle COS ext{ is congruent to } riangle WOS$?

In Problem 4, angles R and G are both classified as ______.

Match each reflection line with its characteristic:

Match the following triangles with their characteristics based on the problems presented:

What can be concluded about segments DE and CE in the first proof?

The statement '∠ANY ≅ ∠YDA' can be proven without establishing a relationship between angles and segments first.

List the given information for the second proof.

In the first proof, the definition of segment bisectors indicates that _______.

Match the following statements to their roles in the proofs:

Which of the following best describes a transformation where a figure is slid to a new location without changing its shape or size?

A reflection transformation results in a figure that is identical to the original figure except for its orientation.

What is the formula for a translation of a geometric figure in the coordinate plane?

A ________ transformation enlarges or reduces a figure but keeps its shape.

Match the type of transformation to its correct description:

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