Based on the information marked in the diagram, AMNP and AQRS must be
congruent.
N
R
ма
P
A. True
B. False

Answer:

Yes, it is true by AAS theorem.

The triangles ΔMNP and ΔQRS are congruent triangles

Transformations change the size or position of shapes. Congruent shapes are identical, but may be reflected, rotated or translated. Scale factors can increase or decrease the size of a shape. Congruent Triangles simply mean the triangles that possess the same size and shape

The three sides are equal (SSS: side, side, side)

Two angles are the same and a corresponding side is the same (ASA: angle, side, angle)

Two sides are equal and the angle between the two sides is equal (SAS: side, angle, side)

A right angle, the hypotenuse and a corresponding side are equal (RHS, right angle, hypotenuse, side)

Given data ,

Let the first triangle be ΔMNP

Now , let the second triangle be ΔQRS

where the measure of angle ∠MNP = measure of angle ∠QRS = 90°

And , the measure of side NP = measure of side RS

And , the measure of ∠NPM = measure of angle ∠RSQ

So , two angles are the same and a corresponding side is the same (ASA: angle, side, angle)

Hence , the triangles are congruent by ASA theorem

To learn more about congruent triangles click :

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a bulleted list of all the important ideas and events in a text in an order that reveals the theme
a bulleted list of all the important ideas and events in a text in an order that reveals the theme

a shorter version of a text that helps readers decide whether they want to read the text
a shorter version of a text that helps readers decide whether they want to read the text

a version of a text that leaves out all the descriptive details in order to highlight the most important ideas
a version of a text that leaves out all the descriptive details in order to highlight the most important ideas

a shortened version of a text that includes the most important events, ideas, and details without a reader’s opinion
a shortened version of a text that includes the most important events, ideas, and details without a reader’s opinion

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