College

Thank you for visiting Given that segment CT bisects angle SCA and that angle S is congruent to angle A prove that triangle SCA is an isosceles triangle with. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!

Given that segment CT bisects angle SCA and that angle S is congruent to angle A, prove that triangle SCA is an isosceles triangle with segment SC congruent to segment CA.

Proof:
Since segment CT bisects angle SCA, angle SCT is congruent to angle ACT. Additionally, we know that angle S is congruent to angle A. By the Angle-Angle-Side (AAS) postulate, triangle SCT is congruent to triangle ACT. Therefore, by the Corresponding Parts of Congruent Triangles are Congruent (CPCTC) theorem, segment SC is congruent to segment CA. Hence, triangle SCA is an isosceles triangle.

Answer :

Final answer:

To prove that triangle SCA is an isosceles triangle with segment SC congruent to segment CA, we need to show that angle SCA is congruent to angle C and that side SC is congruent to side CA. Given that segment CT bisects angle SCA, we can conclude that triangle SCA is an isosceles triangle and that side SC is congruent to side CA.

Explanation:

To prove that triangle SCA is an isosceles triangle with segment SC congruent to segment CA, we need to show that angle SCA is congruent to angle C and that side SC is congruent to side CA.

Given that segment CT bisects angle SCA, we know that angle SCT is congruent to angle CTA. We also know that angle S is congruent to angle A. Therefore, angle SCT is congruent to angle CTA is congruent to angle S is congruent to angle A.

Since angle SCT is congruent to angle CTA and angle S is congruent to angle A, we can conclude that triangle SCA is an isosceles triangle.

Additionally, since segment CT bisects angle SCA, we can also conclude that side SC is congruent to side CA.

Learn more about Triangle Congruence here:

https://brainly.com/question/20521780

#SPJ1

Thank you for reading the article Given that segment CT bisects angle SCA and that angle S is congruent to angle A prove that triangle SCA is an isosceles triangle with. We hope the information provided is useful and helps you understand this topic better. Feel free to explore more helpful content on our website!

Rewritten by : Jeany

Other Questions