if jklm is a rhombus mk = 30, nl = 13, and mean mkl= 41, find each measure.
nk =
jk =
kl =
measure jkm =
measure jml =
measure mlk =
measure mnl =
measure kjl =
Answers
Answer:
A Rhombus j k l m, Diagonals m k and n l intersect each other at point n.
Properties of Rhombus
1. All sides are equal.
2. Diagonals bisect each other at right angles.
3. Opposite sides are Parallel.
∠m k l= 41°
m k=30 cm
m n= n k=15 cm→→Diagonals bisect each other
n l = n j = 13 cm →→→Diagonals bisect each other
In right Δ m n l,
∠ m n l= 90°
By Pythagoras Theorem
(m l)²=(m n)²+(n l)²
(m l)²= (15)²+(13)²
(ml)²=225 + 169
(ml)²=394
m l =√394
m l=19.84 cm
So, m l=j k =k l= 19.8 4 cm
Also,In Δ n k l
90°+41° +∠JLK=180°
∠j l k=180°-131°
∠ j l k=49°
In Δn j k and Δ n k l
n j= n l→→Diagonals bisect each other at right angles.
∠j n k=∠k n l=90°→→Diagonals bisect each other at right angles.
side n k is common.
Δn j k ≅ Δ n k l →→[SAS]
∠n k l = ∠ n j k→→→→[CPCT]
∠n l k =∠ n k j→→→→CPCT
As, opposite sides of rhombus are parallel, that is , m l║ j k and m j║l k, and m k and j l are Transversal.So alternate interior angles are equal.
∠m k j=∠ k m l=49°
∠j m k=∠m k l=41°
∠m j l=∠k l j=49°
∠ m l j=∠k j l =41°
