Math Problem Statement
Prove the congruency in each
Solution
The image you've uploaded contains four geometric diagrams, each of which seems to ask for a proof of congruency between triangles based on given information. I will go through each one and provide the steps required to prove the congruency of the triangles.
Diagram 1.1:
Given: , is common, and .
Proof:
- is common (Shared side).
- (Given).
- (Given).
- By the SAS (Side-Angle-Side) congruence rule, .
Diagram 1.2:
Given: , , and .
Proof:
- (Given).
- (Given).
- (Given).
- By the ASA (Angle-Side-Angle) congruence rule, .
Diagram 1.3:
Given: , , and .
Proof:
- (Given).
- (Given).
- (Given).
- By the SAS (Side-Angle-Side) congruence rule, .
Diagram 1.4:
Given: , , and .
Proof:
- (Given).
- (Given).
- (Given).
- By the ASA (Angle-Side-Angle) congruence rule, .
These steps establish the congruency of the triangles in each of the diagrams provided. Let me know if you need further clarification or a more detailed explanation.
Would you like any additional details or have any questions?
Here are five questions you might find useful:
- How can the ASA and SAS congruence rules be applied in other geometric proofs?
- What are other congruence rules for triangles besides ASA and SAS?
- How can you determine when to use which congruence rule?
- What is the significance of a common side in proving congruence?
- How does angle bisector theorem apply in triangle congruency?
Tip: When working on geometric proofs, always start by identifying the given information and the goal, then match them with the appropriate congruence rules (like SSS, SAS, ASA, or AAS).
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Math Problem Analysis
Mathematical Concepts
Geometry
Triangle Congruence
Formulas
-
Theorems
ASA (Angle-Side-Angle) congruence rule
SAS (Side-Angle-Side) congruence rule
Suitable Grade Level
High School