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1. when using the asa method, what is the significance of the included …

Question

  1. when using the asa method, what is the significance of the included side?

a. it determines the height of the triangle
b. it is always horizontal
c. it connects the two given angles
d. it is the longest side of the triangle

  1. which postulate can be used to prove that two triangles are congruent if two sides and the included angle are known?

a. asa
b. sss
c. aas
d. sas

  1. which term describes triangles that have the same shape but different sizes?

a. congruent
b. equivalent
c. identical
d. similar

  1. which method can uniquely determine a triangle with the least amount of information?

a. sss
b. ssa
c. asa
d. sas

  1. the sss method is especially effective in scenarios where:

a. angles need to be precise
b. the shape must be strictly defined
c. flexibility in design is needed
d. a side needs adjustment

  1. if two angles of one triangle are congruent to two angles of another triangle, the triangles are:

a. scalene
b. congruent
c. similar
d. isosceles

  1. triangles abc and def are congruent by sss with ab = 9 cm, bc = 11 cm, and ca = 13 cm. what is the length of ef?

a. 9 cm
b. 15 cm
c. 13 cm
d. 11 cm

Explanation:

Brief Explanations
  1. In the ASA (Angle - Side - Angle) method, the included side connects the two given angles.
  2. The SAS (Side - Angle - Side) postulate is used when two sides and the included angle are known to prove triangle congruence.
  3. Similar triangles have the same shape but different sizes.
  4. The ASA method can uniquely determine a triangle with relatively less information compared to some other methods.
  5. The SSS (Side - Side - Side) method is effective when the shape must be strictly defined.
  6. If two angles of one triangle are congruent to two angles of another triangle, the triangles are similar (by AA similarity criterion).
  7. Since triangles ABC and DEF are congruent by SSS, corresponding sides are equal. BC corresponds to EF. Given BC = 11 cm, so EF = 11 cm.

Answer:

  1. c. It connects the two given angles.
  2. d. SAS
  3. d. Similar
  4. c. ASA
  5. b. The shape must be strictly defined
  6. c. Similar
  7. d. 11 cm