Question

1. rt ⊥ su and sv ≅ vu

2 vr ≅ vr

1. ________
2. ________
3. △svr ≅ △uvr

word bank:
<abc and <adc are right angles <svr and <uvr are right angles vt congruent vt <svr congruent to <uvr sas congruence theorem
symmetric property of congruence <abc congruent to <adc vr congruent to au reflexive property of congruence
vu congruent to td transitive property of congruence

Explanation:

Step1: Use definition of perpendicular lines

Since \(RT\perp SU\), by the definition of perpendicular lines, \(\angle SVR\) and \(\angle UVR\) are right angles.

Step2: Use right - angles congruence theorem

Right angles are congruent. So, \(\angle SVR\cong\angle UVR\)

Step3: Use SAS Congruence Theorem

We have \(SV\cong VU\) (given), \(\angle SVR\cong\angle UVR\) (from step 2), and \(VR\cong VR\) (reflexive property). By the SAS (Side - Angle - Side) Congruence Theorem, \(\triangle SVR\cong\triangle UVR\)

Answer:

1. \(\angle SVR\) and \(\angle UVR\) are right angles
2. \(\angle SVR\cong\angle UVR\)
3. SAS Congruence Theorem