Question

which postulate can be used to prove triangle congruence if three sides are known?
a. asa
b. aas
c. sas
d. sss

in congruent triangles, which parts are always congruent?
a. corresponding sides and angles
b. the hypotenuses
c. only the sides
d. only the angles

what does cpctc stand for?
a. corresponding parts of congruent triangles are similar
b. corresponding parts of congruent triangles are congruent
c. corresponding parts of congruent triangles are co - linear
d. corresponding parts of congruent triangles are equal

which postulate or theorem is typically used to establish triangle congruence before applying cpctc?
a. midpoint theorem
b. pythagorean theorem
c. cpctc itself
d. sas postulate

which triangle congruence postulate or theorem must be proven before using cpctc?
a. reflexive property
b. sss, sas, asa, or aas
c. cpctc itself
d. transitive property

if triangles mno and pqr are congruent by sss with mn = 8 cm, no = 10 cm, and mo = 12 cm, what is the length of pq?
a. 14 cm
b. 10 cm
c. 8 cm
d. 12 cm

in proving congruence, which postulate involves using two angles and the included side?
a. asa

Explanation:

1. First Question:

• ASA (Angle - Side - Angle) and AAS (Angle - Angle - Side) involve angles. SAS (Side - Angle - Side) involves two sides and an included angle. SSS (Side - Side - Side) is used when three sides are known.

1. Second Question:

• By the definition of congruent triangles, corresponding sides and angles are congruent. Hypotenuses are only relevant for right - angled triangles. Saying only sides or only angles is incorrect as both are congruent in congruent triangles.

1. Third Question:

• CPCTC is an abbreviation. The correct full form is “Corresponding Parts of Congruent Triangles are Congruent”.

1. Fourth Question:

• The SAS Postulate (along with SSS, ASA, AAS) is used to establish triangle congruence before applying CPCTC. The Midpoint Theorem and Pythagorean Theorem are not used for triangle congruence in this context, and CPCTC itself is not used to establish congruence initially.

1. Fifth Question:

• To use CPCTC, we first need to prove triangle congruence using SSS, SAS, ASA, or AAS. The Reflexive Property is a property of equality (or congruence) but not a postulate for proving triangle congruence before CPCTC. CPCTC is a result after proving congruence, and the Transitive Property is about equality/congruence of multiple elements but not for proving triangle congruence before CPCTC.

1. Sixth Question:

• If \(\triangle MNO\cong\triangle PQR\) by SSS, then \(MN = PQ\). Given \(MN = 8\mathrm{cm}\), so \(PQ=8\mathrm{cm}\).

1. Seventh Question:

• ASA (Angle - Side - Angle) involves two angles and the included side.

Answer:

1. d. SSS
2. a. Corresponding sides and angles
3. b. Corresponding Parts of Congruent Triangles are Congruent
4. d. SAS Postulate
5. b. SSS, SAS, ASA, or AAS
6. c. 8 cm
7. a. ASA