srk said:
The purpose of this type of proof is to show that two triangles are congruent, meaning they have the same size and shape. This is an important concept in geometry and is used to solve various problems and equations.
To set up a 2-column proof for this problem, you first need to list the given information in the left column and the corresponding statements and reasons in the right column. Then, you can use the properties of congruent triangles to make the necessary statements and proofs.
Some important properties and theorems used in this type of proof include the Side-Side-Side (SSS), Side-Angle-Side (SAS), and Angle-Side-Angle (ASA) congruence postulates, as well as the Reflexive, Symmetric, and Transitive properties of congruence.
Given: Triangle ABC is an equilateral triangle with side length of 5 cm. Triangle DEF has a diameter of 10 cm with side lengths of 5 cm, 5 cm, and 10 cm.
Prove: Triangle ABC is congruent to triangle DEF.
Statements | Reasons
1. Triangle ABC is an equilateral triangle with side length of 5 cm | Given
2. AB = BC = AC = 5 cm | Definition of an equilateral triangle
3. Triangle DEF has a diameter of 10 cm with side lengths of 5 cm, 5 cm, and 10 cm | Given
4. DE = DF = EF = 5 cm | Definition of a diameter
5. Triangle ABC and triangle DEF are both equilateral triangles with congruent sides | Statements 2 and 4
6. Triangle ABC and triangle DEF are congruent by SSS postulate | Statements 2 and 4, and Definition of congruent triangles
This type of proof is useful in many real-life applications, such as construction and engineering. By proving that two triangles are congruent, we can ensure that they have the same size and shape, which is important for stability and strength in structures. It is also used in navigation and surveying to determine distances and angles accurately.
