Provide an example of a triangle congruence statement using AAS.

If $$\triangle ABC$$ has angles $$A = 50^\text{o}$$ , $$B = 60^\text{o}$$ , and side $$AC = 5 cm$$ , and $$\triangle DEF$$ has angles $$D = 50^\text{o}$$ , $$E = 60^\text{o}$$ , and side $$DF = 5 cm$$ , then $$\triangle ABC \text{ is congruent to } \triangle DEF$$ by AAS.

Provide an example of a triangle congruence statement using ASA.

If $$\triangle GHI$$ has angles $$G = 40^\text{o}$$ , $$H = 70^\text{o}$$ , and side $$GH = 6 cm$$ , and $$\triangle JKL$$ has angles $$J = 40^\text{o}$$ , $$K = 70^\text{o}$$ , and side $$JK = 6 cm$$ , then $$\triangle GHI \text{ is congruent to } \triangle JKL$$ by ASA.

What is the significance of the included side in ASA?

In ASA, the included side is the side between the two angles; it is crucial for establishing congruence because it directly connects the two angles.

What is the significance of the non-included side in AAS?

In AAS, the non-included side is the side that is not between the two angles; it is important for establishing congruence when the angles are known.

How can you determine if two triangles are congruent using the information given?

To determine if two triangles are congruent, compare their corresponding sides and angles using the criteria of AAS or ASA.

What is a common misconception about triangle congruence?

A common misconception is that two triangles can be congruent with only one pair of equal sides; at least two angles or two sides must also be equal.

What is the relationship between congruence and similarity in triangles?

Congruence means that two triangles are identical in size and shape, while similarity means that two triangles have the same shape but may differ in size.

Coach E's ASA and AAS

Flashcard

•

Mathematics

•

10th Grade

•

Practice Problem

•

Hard

•

CCSS

HSG.SRT.B.5, 8.G.A.2

Standards-aligned

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14 questions

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FLASHCARD QUESTION

Front

What does AAS stand for in triangle congruence?

Back

AAS stands for Angle-Angle-Side, a criterion for triangle congruence where two angles and the non-included side of one triangle are equal to two angles and the corresponding non-included side of another triangle.

Tags

CCSS.HSG.SRT.B.5

FLASHCARD QUESTION

Front

What does ASA stand for in triangle congruence?

Back

ASA stands for Angle-Side-Angle, a criterion for triangle congruence where two angles and the included side of one triangle are equal to two angles and the corresponding included side of another triangle.

Tags

CCSS.HSG.SRT.B.5

FLASHCARD QUESTION

Front

What is the criteria for two triangles to be congruent using AAS?

Back

Two triangles are congruent using AAS if two angles and a non-included side of one triangle are equal to two angles and the corresponding non-included side of another triangle.

Tags

CCSS.HSG.SRT.B.5

FLASHCARD QUESTION

Front

What is the criteria for two triangles to be congruent using ASA?

Back

Two triangles are congruent using ASA if two angles and the included side of one triangle are equal to two angles and the corresponding included side of another triangle.

Tags

CCSS.HSG.SRT.B.5

FLASHCARD QUESTION

Front

If two triangles have two pairs of equal angles, what can be concluded about their congruence?

Back

If two triangles have two pairs of equal angles, they are congruent by the AAS or ASA criteria.

Tags

CCSS.HSG.SRT.B.5

FLASHCARD QUESTION

Front

Can two triangles be congruent if only one side is equal?

Back

No, two triangles cannot be congruent if only one side is equal; at least two angles or two sides must also be equal.

Tags

CCSS.8.G.A.2

FLASHCARD QUESTION

Front

What does it mean if two triangles are 'not congruent'?

Back

If two triangles are 'not congruent', it means that they do not have the same size and shape, and their corresponding sides and angles are not equal.

Tags

CCSS.8.G.A.2

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