Triangle Inequality & Congruent Triangles Theorems

  • CCSS.Math.Content.HSG
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| Attempts: 486 | Questions: 12 | Updated: Mar 19, 2025
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1)
The shortest side of ΔDEF is ___________.

Explanation

The shortest side of triangle ΔDEF is DE.

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About This Quiz
Triangle Inequality & Congruent Triangles Theorems - Quiz

This will count as DOM # 1: Triangle Congruence.  You MUST show your final score to either Ms. A or Ms. MeGahee.  If you do not show either of us the score, you will receive a 0!  Good luck! You may use your notes / book.        ... see more           see less

2)
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2)

Explanation

not-available-via-ai

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3) Which combination of congruent corresponding parts can you not use to prove two triangles congruent?

Explanation

You remembered that you must have at least one pair of congruent sides.

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4)    by the _______________.

Explanation

The SSS (Side-Side-Side) Postulate states that if three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent. In other words, if all three sides of one triangle have the same length as the corresponding three sides of another triangle, then the two triangles are congruent. This postulate is used to determine congruence between triangles based solely on the lengths of their sides.

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5) By which reason can it be proven that triangles DAB and DAC are congruent?

Explanation

The reason why triangles DAB and DAC can be proven congruent is by using the AAS (Angle-Angle-Side) congruence criterion. This criterion states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent. In this case, the two angles (AAA) are congruent, and the included side (side AD) is congruent. Therefore, by the AAS criterion, triangles DAB and DAC are congruent.

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6) Two triangles are necessarily congruent if and only if __________.

Explanation

Two triangles are necessarily congruent if and only if their corresponding sides and corresponding angles are congruent. This is because congruent triangles have the same shape and size. The corresponding sides of congruent triangles are equal in length, and the corresponding angles are equal in measure. Therefore, if both the sides and angles of two triangles are congruent, then the triangles are necessarily congruent.

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7)

Refer to the figure. Complete the congruence statement 

Explanation

The correct answer is Triangle VUT because the vertices of the triangles are listed in a clockwise order. In congruence statements, the order of the vertices matters, and the given answer follows the correct order.

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8)
Which postulate or theorem shows that 

Explanation

The AAS (Angle-Angle-Side) theorem states that if two angles and a non-included side of one triangle are congruent to the corresponding angles and non-included side of another triangle, then the two triangles are congruent. This theorem is used to prove congruence between triangles when the given information involves two angles and a non-included side.

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9)
Use the triangle inequality to determine the smallest angle in the figure.
∠SCI

Explanation

∠CIS. This angle is opposite from the smallest side. Therefore, according to the triangle inequality, it is the smallest angle.

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10)


ΔSAM≅ΔRAT
Which statement is NOT necessarily true?

Explanation

The statement "MA = TA" is not necessarily true. While it is given that ΔSAM is congruent to ΔRAT, it does not guarantee that the corresponding angles and sides are equal. Therefore, it is not necessary for the measure of angle MA to be equal to the measure of angle TA.

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11)


which pair of triangles would you use ASA to prove the congruence of the 2 triangles?

Explanation

The triangles shown in choice C can be proven congruent by ASA. The triangles have 2 pairs of congruent angles and pair of congruent included sides.

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12) List the sides of the triangle in order from SHORTEST to LONGEST.




Explanation

The sides of the triangle in order from shortest to longest are BA, BC, and AC.

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The shortest side of ΔDEF is ___________.
Which combination of congruent corresponding parts can...
   by the _______________.
By which reason can it be proven that triangles DAB and DAC are...
Two triangles are necessarily congruent if and only if __________.
Refer to the figure. Complete the congruence statement 
Which postulate or theorem shows that 
Use the triangle inequality to determine the smallest angle in the...
ΔSAM≅ΔRATWhich statement is NOT necessarily true?
Which pair of triangles would you use ASA to prove the congruence of...
List the sides of the triangle in order from SHORTEST to LONGEST.
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