# Congruence of ACB & CED: Similarity Chapter

• MHB
• slwarrior64
In summary, the conversation discusses the use of symbols ACB and CED to represent congruent triangles in a diagram. It is mentioned that the concept of similarity is not applicable in this situation and that triangle ABC is a right triangle. It is also implied that triangle CED is a right triangle, as otherwise the problem would be unsolvable. It is stated that angles ACB and CED are congruent, leading to the conclusion that angles CAB and DCE are also congruent. It is then deduced that angle ACE is a right angle, making triangle ACE a right triangle with sides measuring 7 and 24. The length of AE can be found using the Pythagorean theorem.
slwarrior64

Only use that ACB and CED are congruent, not any other symbols in the diagram.

I don't think "similarity" is useful here (and the two triangles are definitely NOT "congruent". We are given that triangle ABC is a right triangle. (It is not specifically said that triangle CED is a right triangle but if angle CDE is not a right angle this problem is un-doable.) Angle ACB is congruent to angle CED. Since both triangles are right angles it follows that angles CAB and DCE are congruent and then that angle ACE is a right angle! So triangle ACE is a right triangle with legs of length 7 and 24. The length of AE follows from the Pythagorean theorem.

## 1. What is the definition of congruence?

Congruence is a term used in geometry to describe two figures that have the same size and shape. In other words, if two figures are congruent, they are identical in every way.

## 2. How do you prove that two triangles are congruent?

There are several ways to prove that two triangles are congruent, including using the Side-Side-Side (SSS), Side-Angle-Side (SAS), Angle-Side-Angle (ASA), or Hypotenuse-Leg (HL) congruence criteria. These criteria involve comparing the corresponding sides and angles of the two triangles to show that they are equal.

## 3. What is the difference between congruence and similarity?

Congruence and similarity are both terms used to describe the relationships between two figures. While congruence means that two figures are identical in every way, similarity means that two figures have the same shape, but may differ in size. In other words, congruent figures are always similar, but similar figures are not always congruent.

## 4. How does the concept of congruence apply to the ACB and CED triangles?

In this context, congruence refers to the fact that the two triangles have the same size and shape. This means that the corresponding sides and angles of the ACB and CED triangles are equal, making them congruent triangles.

## 5. Can two triangles be congruent if they have different orientations?

Yes, two triangles can be congruent even if they have different orientations. As long as the corresponding sides and angles are equal, the triangles are considered congruent. This means that one triangle can be rotated, reflected, or translated to match the other triangle, and they will still be congruent.

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