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Questions and Answers
What does the SSS Postulate state?
Which postulate states that two triangles are congruent if two angles and the included side are congruent in each triangle?
What does CPCTC stand for in geometry?
Which theorem is not a postulate but a theorem?
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If two triangles have the same corresponding parts (angles and sides), what can be concluded?
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What is the SAS Postulate used for in geometry?
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Which criterion involves proving two triangles are congruent by showing that they have equal corresponding sides and angles?
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What is the main difference between the ASA Postulate and AAS Theorem?
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Which postulate considers the equality of two angles and a non-included side?
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If two triangles have all three sides equal in length, what criterion can be used to prove their congruence?
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Study Notes
Triangle Congruence: Key Criteria
Understanding how to prove two triangles are congruent is essential in geometry. The congruence of triangles is based on their corresponding sides and angles being equal. There are various criteria to determine congruence, each offering a different perspective on the equivalence of triangles.
Side-Side-Side (SSS) Postulate
Two triangles are congruent if all three sides have equal lengths. The SSS postulate is the most straightforward method to prove congruence.
Side-Angle-Side (SAS) Postulate
Two triangles are congruent if two sides and the angle between them are congruent in each triangle.
Angle-Side-Angle (ASA) Postulate
Two triangles are congruent if two angles and the included side are congruent in each triangle.
Angle-Angle-Side (AAS) Theorem
Two triangles are congruent if two angles and a non-included side are congruent in each triangle. Note that this is not a postulate but a theorem.
Hypotenuse-Leg (HL) Theorem for Right Triangles
Two right triangles are congruent if their hypotenuse and leg are equal.
Corresponding Parts of Congruent Triangles are Congruent (CPCTC)
If two triangles are congruent, their corresponding parts (angles and sides) will be congruent.
Congruence Does Not Depend on Angle Order
When proving congruence using the ASA, SAS, or AAS criteria, the order of the vertices is not important.
Congruence is Not Proven by AAA, SAA, or HL Alone
Two triangles cannot be proven congruent using only the angle measures (AAA), side opposite an angle (SAA), or hypotenuse and an angle in a right triangle (HL) criteria alone.
Equivalent Conditions for Right Triangles
For right triangles, the HL, LL, and AL criteria are equivalent to each other.
Congruence Does Not Depend on Drawing Scale
The congruence of triangles is not dependent on the scale of the drawing.
By understanding these criteria, you'll be able to prove the congruence of triangles in various geometrical situations.
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Description
Learn about the key criteria for proving triangle congruence, including SSS, SAS, ASA, AAS, HL, CPCTC, and more. Explore how corresponding sides and angles determine the equivalence of triangles, regardless of the drawing scale or angle order.
