Question

1. if △pqr and △stu are congruent by asa, and ∠p ≅ ∠s and ∠q ≅ ∠t, which side must also be congruent?

a. pq and st
b. qr and tu
c. qr and su
d. pr and su

1. what type of information is required to construct a triangle using the sas method?

a. two sides and the included angle
b. two sides and a non-included angle
c. two angles and the included side
d. three sides

1. if △abc has sides ab = 6 cm, ac = 8 cm, and ∠bac = 70°, which of the following triangles is congruent to △abc by sas?

a. △def with de = 6 cm, df = 9 cm, ∠edf = 70°
b. △def with de = 7 cm, df = 8 cm, ∠edf = 70°
c. △def with de = 6 cm, df = 8 cm, ∠edf = 70°
d. △def with de = 6 cm, df = 8 cm, ∠edf = 75°

1. when constructing a triangular roof frame, which method is typically used?

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

1. which of the following conditions must be met to use the sss triangle congruence rule?

a. all three pairs of corresponding angles must be equal.
b. all three pairs of corresponding sides must be equal.
c. two angles and the included side must be equal.
d. two sides and the included angle must be equal.

1. what is the included angle in △abc if ab = 5 cm, ac = 7 cm, and ∠bac = 80°?

a. ∠bac
b. ∠bca
c. ∠abc
d. ∠acb

Explanation:

22.

In the ASA (Angle - Side - Angle) congruence criterion, the side between the two congruent angles must be congruent. Given that \(\angle P\cong\angle S\) and \(\angle Q\cong\angle T\), the side between \(\angle P\) and \(\angle Q\) in \(\triangle PQR\) is \(PQ\), and the side between \(\angle S\) and \(\angle T\) in \(\triangle STU\) is \(ST\). So \(PQ\) and \(ST\) must be congruent.

The SAS (Side - Angle - Side) method for triangle congruence requires two sides and the included angle (the angle between the two sides) to be known.

For the SAS congruence criterion, we need two sides and the included angle to be equal. In \(\triangle ABC\), \(AB = 6\mathrm{cm}\), \(AC=8\mathrm{cm}\), \(\angle BAC = 70^{\circ}\). In \(\triangle DEF\), if \(DE = 6\mathrm{cm}\), \(DF = 8\mathrm{cm}\), \(\angle EDF=70^{\circ}\), then by SAS (\(AB = DE\), \(\angle BAC=\angle EDF\), \(AC = DF\)), \(\triangle ABC\cong\triangle DEF\)

Answer:

a. \(PQ\) and \(ST\)

23.