Questions and Answers
If QRS = DEF, name three pairs of corresponding congruent angles.
A.Q = D, R = E, S = F
If QRS = XYZ, list two pairs of congruent sides and two pairs of congruent angles.
QR = XY, RS = YZ; Q = X, S = Z
Which side or angle is common to both TXU and TVS?
B.T
Using CPCTC, name the congruent parts of ABC and QRS that are not labeled as congruent in the diagram.
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Given that FG = IJ, show that GH = JK.
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Which of the following is common to both PQV and PRT?
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Given that SU is the perpendicular bisector of TV, which of the following statements is true?
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Given that Q = R and PV = PT, show that PQ = PR.
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Which of the following is common to both ADC and BCD?
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Given the diagram above and the fact that BCD = ADC, show that B = A.
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Identify the steps for proving AD = DC.
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Given that IFG = HGF and I = H, show that FJI = GJH.
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Name the corresponding congruent sides of the two congruent triangles shown above.
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ABE is isosceles with base BE. Given that B = E and BD = BC, show that ACD = ADC.
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Which of the following is common to both BAD and BAC?
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Study Notes
Congruent Triangles: CPCTC Overview
- CPCTC stands for "Corresponding Parts of Congruent Triangles are Congruent," a key principle in geometry.
- Congruent triangles have equal corresponding angles and sides.
Corresponding Angles and Sides
- In triangles QRS and DEF, angles Q, R, S correspond to angles D, E, F respectively.
- For triangles QRS and XYZ, sides QR, RS, and angles Q, S can be stated as congruent to respective parts of triangle XYZ.
Common Parts in Triangles
- B.T is the common angle between triangles TXU and TVS.
- DC is the common side between triangles ADC and BCD.
CPCTC Applications
- If triangles are proven congruent, all corresponding parts also must be congruent, not just the labeled ones.
- Reflexive property asserts that side CD in triangles involving ACD and ADC is congruent because both triangles share this side.
Proving Congruence
- When given congruent angles and sides (e.g., SU as a perpendicular bisector), corresponding angle relationships can be established using CPCTC.
- Congruent relationships, such as FJI = GJH, can be derived from vertical angles and shared sides.
Isosceles Triangle Properties
- In isosceles triangle ABE, base BE leads to two congruent angles at points B and E, crucial for proving the congruence of associated segments.
- The congruence of angles and sides is essential in deriving equality statements regarding lines in the triangles, such as AD = DC.
Proof Structure
- The steps for proving congruence often involve establishing the equality of shared sides (reflexive property) and applying congruence conditions like SAS (Side-Angle-Side) or AAS (Angle-Angle-Side).
Key Takeaways
- Reflexive properties, congruent angles, and parallel line relationships are fundamental for establishing triangle congruence.
- Understanding the relationships and proofs involved in CPCTC strengthens the foundation of geometric principles related to triangles.
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Description
This quiz covers the concept of CPCTC, which means 'Corresponding Parts of Congruent Triangles are Congruent.' It explains how angles and sides of congruent triangles correspond to one another and provides examples of proving congruence using various properties. Test your understanding of this important geometric principle!
