Math Problem Statement
solve
Solution
The diagram provided shows two triangles, and , sharing a common side , with and being a common side for both triangles. Additionally, as they form right angles at point .
To prove that these triangles are congruent, we can use the SAS (Side-Angle-Side) Postulate. Here’s why:
- Side: is shared by both triangles.
- Angle: , both are right angles.
- Side: , as given by the tick marks showing they are equal in length.
Since we have two sides and the included angle congruent, the SAS (Side-Angle-Side) postulate applies.
The correct answer is SAS.
Would you like more details, or do you have any further questions?
Here are 5 related questions you can explore:
- What other methods can be used to prove triangle congruence?
- Can the AAS (Angle-Angle-Side) postulate apply here?
- Why is SSA (Side-Side-Angle) not a valid congruence postulate?
- How does the HL (Hypotenuse-Leg) theorem apply to right triangles?
- How do you differentiate between congruent and similar triangles?
Tip: Always check for shared sides or angles when proving triangle congruence, as these often provide key clues.
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Math Problem Analysis
Mathematical Concepts
Congruent Triangles
Geometric Postulates
Triangle Properties
Formulas
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Theorems
SAS (Side-Angle-Side) Postulate
Triangle Congruence
Suitable Grade Level
Grades 8-10