If $$\triangle ABC \text{ and } \triangle DEF$$ are congruent, what can be said about their corresponding parts?

If $$\triangle ABC \text{ and } \triangle DEF$$ are congruent, then their corresponding sides and angles are equal: $$AB = DE, BC = EF, CA = FD$$ and $$\triangle A = \triangle D, \triangle B = \triangle E, \triangle C = \triangle F$$ .

How can you prove triangles are congruent using the SSS criterion?

To prove triangles are congruent using the SSS criterion, measure all three sides of both triangles and show that they are equal.

What additional information is needed to prove $$\triangle EFD \text{ congruent to } \triangle EID$$ by HL?

To prove $$\triangle EFD \text{ congruent to } \triangle EID$$ by HL, you need to show that $$ar{EF} \text{ is congruent to } ar{EI}$$ .

If two angles of a triangle are known, how can the third angle be found?

The third angle can be found using the triangle sum theorem, which states that the sum of the angles in a triangle is always $$180^\text{°}$$ . Thus, $$\text{Third Angle} = 180^\text{°} - (\text{Angle 1} + \text{Angle 2})$$ .

What is the relationship between the angles and sides in congruent triangles?

In congruent triangles, corresponding angles are equal and corresponding sides are equal.

How do you solve for an unknown angle in a triangle?

To solve for an unknown angle in a triangle, use the triangle sum theorem or the properties of congruent triangles to set up an equation.

What is the significance of the congruence symbol (≅)?

The congruence symbol (≅) indicates that two geometric figures are congruent, meaning they have the same shape and size.

What is the difference between congruence and similarity in triangles?

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

Triangle Congruence Review

Flashcard

•

Mathematics

•

10th Grade

•

Practice Problem

•

Hard

•

CCSS

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

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FLASHCARD QUESTION

Front

What does congruence mean in geometry?

Back

Congruence in geometry means that two figures have the same shape and size. This can be shown through various congruence criteria.

Tags

CCSS.8.G.A.2

FLASHCARD QUESTION

Front

What are the criteria for triangle congruence?

Back

The main criteria for triangle congruence are: SSS (Side-Side-Side), SAS (Side-Angle-Side), ASA (Angle-Side-Angle), AAS (Angle-Angle-Side), and HL (Hypotenuse-Leg for right triangles).

Tags

CCSS.HSG.SRT.B.5

FLASHCARD QUESTION

Front

What is the SSS congruence criterion?

Back

The SSS (Side-Side-Side) criterion states that if three sides of one triangle are equal to three sides of another triangle, then the triangles are congruent.

Tags

CCSS.HSG.SRT.B.5

FLASHCARD QUESTION

Front

What is the SAS congruence criterion?

Back

The SAS (Side-Angle-Side) criterion states that if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the triangles are congruent.

Tags

CCSS.HSG.SRT.B.5

FLASHCARD QUESTION

Front

What is the ASA congruence criterion?

Back

The ASA (Angle-Side-Angle) criterion states that if two angles and the included side of one triangle are equal to two angles and the included side of another triangle, then the triangles are congruent.

Tags

CCSS.HSG.SRT.B.5

FLASHCARD QUESTION

Front

What is the AAS congruence criterion?

Back

The AAS (Angle-Angle-Side) criterion states that 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, then the triangles are congruent.

Tags

CCSS.HSG.SRT.B.5

FLASHCARD QUESTION

Front

What is the HL congruence criterion?

Back

The HL (Hypotenuse-Leg) criterion applies to right triangles and states that if the hypotenuse and one leg of one right triangle are equal to the hypotenuse and one leg of another right triangle, then the triangles are congruent.

Tags

CCSS.HSG.SRT.B.5

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