Question

Look at pic down underrr

Answer 1

Answer:

Triangle rsu = Triangle tus

Statements Reasons

UR ≅ TS  Definition of Rectangle

US ≅ US Reflexive Property

<U, <T, <R, <S are all congruent and right angles

Definition of Rectangle

ΔRSU ≅ ΔTUS Side, Angle, Side

UR ≅ TS     CPCTC

Just draw a reverse angle,hence you get comparison.

So, satisfying S-S-S

RUS  ≅ SUT

RSU ≅ TUS

So, angle

URS = angle TUS

2. Pythagoras Theorem

Triangle RUS

A^2 + B^2 = C^2

Uu^2 + Ss^2 = Rr^2

√Rr = Rr^2 = x

Triangle TUS

A^2 + B^2 = C^2

Ss^2 + Uu^2 = Tt^2

√Tt = Tt^2 = x

UR measure / sin (60) x (90) = US measure.

ST measure / sin (60) x (90) = US measure.

Proves angles RSU = 30 degree

Proves angles  TUS = 30 degree

As all adjacent angles in a triangle add up to 180 degree.