Triangle Congruence

Title: Triangle Congruence

Question 1:
Sunita is building a kite with two congruent sides and two congruent angles. Which criterion for congruent triangles should she use to ensure that her kite is symmetrical? Explain your answer.
Answer 1:
Sunita should use the SAS (Side-Angle-Side) criterion for congruent triangles. This criterion states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent. By using SAS, Sunita can ensure that her kite has two congruent sides and two congruent angles, making it symmetrical.

Question 2:
Rohan wants to prove that two triangles are congruent. He knows that all three sides of one triangle are congruent to the corresponding sides of the other triangle. Which criterion for congruent triangles should he use? Explain your answer.
Answer 2:
Rohan should use the SSS (Side-Side-Side) criterion for congruent triangles. This criterion states that if three sides of one triangle are congruent to the corresponding sides of another triangle, then the two triangles are congruent. By knowing that all three sides of one triangle are congruent to the corresponding sides of the other triangle, Rohan can prove that the two triangles are congruent using SSS.

Question 3:
Riya is trying to prove that two triangles are congruent using an angle, a side, and another angle of one triangle being congruent to the corresponding parts of the other triangle. Which criterion for congruent triangles should she use? Explain your answer.
Answer 3:
Riya should use the ASA (Angle-Side-Angle) criterion for congruent triangles. This criterion states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent. By using ASA, Riya can prove that the two triangles are congruent based on the given information.

Question 4:
In a school playground, two children are playing on the seesaw. The seesaw is perfectly balanced, with one child on each side. Explain how you can prove that the triangles formed by the children's positions are congruent.
Answer 4:
To prove that the triangles formed by the children's positions on the seesaw are congruent, we can use the SAS (Side-Angle-Side) criterion. Since the seesaw is perfectly balanced, both sides of the seesaw are at the same height. This means that the vertical sides of the triangles (corresponding to the seesaw) are congruent. Additionally, the angles formed by the children's positions on the seesaw are congruent because the seesaw is balanced. Lastly, the distance between the children (the base of the triangles) is the same on each side. By using the SAS criterion, we can conclude that the triangles formed by the children's positions on the seesaw are congruent.

Question 5:
In a construction project, two identical houses are being built side by side. Explain how you can prove that the triangles formed by the rooftops of the houses are congruent.
Answer 5:
To prove that the triangles formed by the rooftops of the houses are congruent, we can use the SSS (Side-Side-Side) criterion. Since the houses are identical, all three sides of one rooftop will be congruent to the corresponding sides of the other rooftop. This is because the houses are built with the same dimensions and angles. By using the SSS criterion, we can conclude that the triangles formed by the rooftops of the houses are congruent.

Remember, in mathematics, congruent triangles have the same shape and size, and proving their congruence helps us understand the properties and relationships between different geometric figures.