https://file.aiquickdraw.com/mathbot/file/17297133833433s135mwb.jpg

In the triangles, AB
cm, A
cm, and
cm. To prove △ABC≅△ADE by the SAS Congruence Postulate, AC must equal [blank] cm.

Enter your answer as the value that correctly fills in the blank.

In the diagram, we are given two triangles, \( \triangle ABC \) and \( \triangle ADE \), with some side lengths labeled. The goal is to prove that \( \triangle ABC \cong \triangle ADE \) using the SAS (Side-Angle-Side) Congruence Postulate.

### Information provided:
- \( AB = 3 \) cm
- \( AD = 3 \) cm
- \( AE = 4 \) cm

For the SAS postulate to hold, we need:
- Two pairs of corresponding sides to be equal.
- The angle between these pairs to be equal.

From the diagram:
- Side \( AB \) corresponds to side \( AD \) (both are given as 3 cm).
- Side \( AE \) corresponds to side \( AC \), but the length of \( AC \) is not provided. This is the missing value we need to find.

### Congruence Postulate:
For \( \triangle ABC \cong \triangle ADE \), \( AC \) must correspond to side \( AE \), which is given as 4 cm.

Thus, \( AC \) must be \( \boxed{4} \) cm.

Would you like more details or have any questions?

### Follow-up Questions:
1. How does the SAS Congruence Postulate work in proving triangle congruence?
2. What are the other methods to prove triangle congruence besides SAS?
3. Can you identify any other pairs of congruent triangles in the diagram?
4. How can we prove that the angles \( \angle BAC \) and \( \angle DAE \) are congruent?
5. What are the implications of congruent triangles in geometry problems?

### Tip:
When using the SAS Congruence Postulate, always ensure that the angle you are considering is **between** the two pairs of sides you're comparing.

In the triangles, AB = 3 cm, AD = 3 cm, and AE = 4 cm. To prove △ABC≅△ADE by the SAS Congruence Postulate, AC must equal [blank] cm.

Learn how to prove △ABC ≅ △ADE using the SAS Congruence Postulate. This problem covers key concepts in triangle congruence, specifically the application of the SAS (Side-Angle-Side) postulate. Suitable for students in Grades 7-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation