30 60 90 triangles (quick answers please)

1) EF = 2 and DF = 4

2) KL = 4√3 and JL = 8

3) ST = 6 and RS = 6√3

4) PQ = 4.5√3 and RQ = 4.5

Step-by-step explanation:

Rules for special triangles 30°,60°,90° :

1) DE = 2√3 is opposite to 60°

⇒ 2√3 = a√3

⇒ a = 2

EF = a which is opposite to 30°.

⇒ EF = 2

DF = 2a which is opposite to 90°.

⇒ DF = 4

2) KJ = 4 is opposite to 30°

⇒ a = 4

KL = a√3 which is opposite to 60°.

⇒ KL = 4√3

JL = 2a which is opposite to 90°.

⇒ JL = 8

3) RT = 12 is opposite to 90°

⇒ 2a = 12

⇒ a = 6

ST = a which is opposite to 30°.

⇒ ST = 6

RS = a√3 which is opposite to 60°.

⇒ RS = 6√3

4) PR = 9 is opposite to 90°

⇒ 2a = 9

⇒ a = 4.5

PQ = a√3 which is opposite to 60°.

⇒ PQ = 4.5√3

RQ = a which is opposite to 30°.

⇒ RQ = 4.5

step-by-step explanation:

two pairs of adjacent sides are of equal length. this implies that one diagonal divides the kite into congruent triangles, and so the angles between the two pairs of equal sides are equal in measure. it also implies that the diagonals are perpendicular.

answer: list the statements and i will follow up!

step-by-step explanation: