Asap
given: rt || sp, rq ≅ qp, rp bisects st at q
prove: δrqt ≅ δpqs

tamir is working to prove the triangles congruent using sas. after stating the given information, he states that tq ≅ qs by the definition of segment bisector. now he wants to state that ∠rqt ≅ ∠pqs. which reason should he use?

SAS theorem states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then these two triangles are congruent.

1. RQ ≅ QP (given)

2. If RP bisects ST at Q, then  TQ ≅ QS (by the definition of segment bisector).

3. ∠RQT,  ∠PQS are vertical angles (angles that are vertically opposite to each other when lines PR and ST intersect, Q is the common vertex).

∠RQT ≅ ∠PQS  (by the vertical angles theorem).

Vertical angles theorem  states that vertical angles are always congruent.

According to SAS theorem, ΔRQT ≅ ΔPQS.

vertical angles theorem

step-by-step explanation:

12: 00 p.m. to 7: 00 p.m. is a total of 7 hours.

4: 00 p.m. to 7: 00 p.m. is a total of 3 hours.

this means that from 4: 00 p.m to 7: 00 p.m. this represents 3/7 of what was lost from 12: 00 p.m. to 7: 00 p.m.

after knowing this, after doing 11,600 - 6,800 = 4,800

4,800 represents 3/7 of what was lost for 7 hours.

we then divide 4,800 by 3 which gets 1,600.

because we know that 1,600 represents 1/7 of how much water was lost, we just have to multiply by 7, which gets 11,200.   after adding 11,200 to how much water was left at 7: 00 p.m. which was 6,800. 11,200 + 6,800 = 18,000

this means that the pool originally had 18,000 gallons in the pool.

you can also check your work by doing 18,000 - 4(1600), which becomes           1800 - 6400 which gets you 11,600.