https://file.aiquickdraw.com/mathbot/file/17271121430801jy89keb.jpg

M is the midpoint of AD.

Triangles A B M and D C M are connected at point M. Sides A B and C D are congruent. The lengths of sides B M and M C are 27.

What single transformation is required to map one of these congruent triangles onto the other?

A.     Reflection
B.     Rotation
C.     Translation
D.     Dilation

In this problem, we are given two triangles \( \triangle ABM \) and \( \triangle DCM \), which share point \( M \) as their vertex. We know that the sides \( AB \) and \( CD \) are congruent, and \( BM = MC = 27 \). The problem asks us to determine which transformation will map one triangle onto the other.

Given the image and information:

- The triangles are congruent by the **Side-Side-Side (SSS)** congruence criterion: \( AB = CD \), \( BM = MC \), and both triangles share side \( AM = DM \).
- Since these triangles share a vertex at \( M \), and appear symmetric about a vertical line passing through \( M \), the appropriate transformation would be a **reflection**.

The correct transformation to map one triangle onto the other is:

**A. Reflection**

Would you like further details or explanations about reflections or congruence? 

Here are five related questions to deepen your understanding:
1. How can you identify a line of reflection between two congruent triangles?
2. What are other types of transformations besides reflection, and how do they differ?
3. Can two triangles still be congruent if their angles differ but their sides are the same?
4. What conditions must be met for triangles to be congruent under the SSS criterion?
5. How can you verify if two figures are congruent using transformations?

**Tip:** When solving geometric problems involving congruence, always check for symmetry, which often suggests reflection as a transformation!

M is the midpoint of AD. Triangles A B M and D C M are connected at point M. Sides A B and C D are congruent. The lengths of sides B M and M C are 27. What single transformation is required to map one of these congruent triangles onto the other? A. Reflection B. Rotation C. Translation D. Dilation

Learn how to solve a problem involving two congruent triangles ABM and DCM connected at midpoint M. This problem covers concepts of triangle congruence, transformations, and the SSS Congruence Criterion. Suitable for students in Grades 8-10.

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