Math / Geometry

QuestionCan you conclude that these triangles are congruent? yes no

Studdy Solution

STEP 1

1. Triangles QMS and NMP are given.
2. Sides QM and NM are marked as equal.
3. Sides SM and PM are marked as equal.
4. The triangles share the common side, $\overline{MP}$ .

STEP 2

1. Identify the congruence criteria.
2. Check if the criteria are satisfied.
3. Conclude whether the triangles are congruent.

STEP 3

Identify the congruence criteria that can be used to determine if two triangles are congruent. Common criteria include: - Side-Side-Side (SSS) - Side-Angle-Side (SAS) - Angle-Side-Angle (ASA) - Angle-Angle-Side (AAS) - Hypotenuse-Leg (HL) for right triangles

STEP 4

Check if the criteria are satisfied: - We have two pairs of equal sides: $\overline{QM} = \overline{NM}$ and $\overline{SM} = \overline{PM}$ . - The triangles share the common side $\overline{MP}$ .
This satisfies the Side-Side-Side (SSS) criterion for triangle congruence.

STEP 5

Conclude whether the triangles are congruent: Since the SSS criterion is satisfied, we can conclude that triangles QMS and NMP are congruent.
Answer: Yes

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