Give me an example about corresponding parts of congruent triangles.
Understand the Problem
The question is asking for an example of the corresponding parts of congruent triangles. This refers to the principle that if two triangles are congruent, then their corresponding sides and angles are also congruent (equal).
Answer
If $\triangle ABC \cong \triangle DEF$, then $AB = DE$ and $\angle A = \angle D$.
Answer for screen readers
If $\triangle ABC \cong \triangle DEF$, then $AB = DE$ and $\angle A = \angle D$ are examples of corresponding parts of congruent triangles.
Steps to Solve
- Define Congruent Triangles
Two triangles are congruent if they have the same size and shape. This means that all corresponding sides and all corresponding angles are equal.
- Corresponding Sides
Corresponding sides are the sides that are in the same position in two different figures. If $\triangle ABC \cong \triangle XYZ$, then: - Side $AB$ in $\triangle ABC$ corresponds to side $XY$ in $\triangle XYZ$. - Side $BC$ in $\triangle ABC$ corresponds to side $YZ$ in $\triangle XYZ$. - Side $CA$ in $\triangle ABC$ corresponds to side $ZX$ in $\triangle XYZ$. Therefore, $AB = XY$, $BC = YZ$, and $CA = ZX$.
- Corresponding Angles
Corresponding angles are the angles that are in the same position in two different figures. If $\triangle ABC \cong \triangle XYZ$, then: - Angle $A$ in $\triangle ABC$ corresponds to angle $X$ in $\triangle XYZ$. - Angle $B$ in $\triangle ABC$ corresponds to angle $Y$ in $\triangle XYZ$. - Angle $C$ in $\triangle ABC$ corresponds to angle $Z$ in $\triangle XYZ$. Therefore, $\angle A = \angle X$, $\angle B = \angle Y$, and $\angle C = \angle Z$.
- Example of Corresponding Parts
Given $\triangle ABC \cong \triangle DEF$, an example of corresponding parts is: - Side $AB$ corresponds to side $DE$, so $AB = DE$. - Angle $A$ corresponds to angle $D$, so $\angle A = \angle D$.
If $\triangle ABC \cong \triangle DEF$, then $AB = DE$ and $\angle A = \angle D$ are examples of corresponding parts of congruent triangles.
More Information
The concept of corresponding parts of congruent triangles is often abbreviated as CPCTC (Corresponding Parts of Congruent Triangles are Congruent). This principle is fundamental in geometry and is used to prove various theorems and solve problems involving congruent triangles.
Tips
A common mistake is confusing corresponding parts. For example, if $\triangle ABC \cong \triangle DEF$, it's incorrect to say that side $AB$ corresponds to side $EF$. Always ensure the vertices are listed in the correct order to determine corresponding sides and angles accurately.
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