Question

Please help me do my math home work i am stuck you can see the questions in the given below attachment.

Answer 1

Step-by-step explanation:

1)Given that ∆PsQ=∆STU under ASA property then

=>Corresponding sides are equal

Corresponding angles are equal

=>Angle Q= angle T

angle R=angle U

=>angle U=30°

x=30°

and the sum of all angles in a triangle =180°

=>LP+LQ+LR=180°

=>LP+60°+30°=180°

=>LP+90°=180°

=>LP=180°-90°

=>LP=90°

LP=LS

=>Y=90°

2)In two triangles ,∆PSQ and ∆PSR

PQ=PR=6.5cm

LPSQ=LPSR=90°

PS=PS(common side)

By RHS property,

∆PSQ is congruent to ∆PSR

and QS=QR

(congruent parts are equal in Congruent triangles)

=>∆PSQ=∆PSR

3)From the two triangles ∆LMN and ∆ONM

LM=ON(given)

LN=OM(given)

MN=MN(common side)

By SSS Property,

∆LMN is congruent to ∆ONM