Respuesta :

carlafossil320
Statement D must be true. According to the given information, triangles JKM and LKM are congruent and the form triangle JKL, which is an equilateral triangle. That means that angles K, J and L are 60, so angles JKM and LKM are both 30°. This leaves two 30-60-90 triangles, JKM and LKM.
varshamittal029

The correct option is option D: ΔJKM is 30-60-90 triangle.

What is equilateral triangle?

The triangle whose all the three sides are equal is called equilateral triangle.

Three angles of an equilateral triangle is also equal which is 60°.

In ΔJKL, KM is perpendicular to JL i.e. KM⊥JL

∠KMJ=∠KML=90°

Between ΔJKM and ΔKLM

KJ=KL (As equilateral triangles ΔJKL has all sides equal)

∠KJM=∠KLM (=60°)

∠KMJ=∠KML=90°

ΔJKM ≅ ΔKLM (Angle-Angle-side)

ΔJKM and ΔKLM are congruent.

⇒∠JKM=∠LKM

As ∠JKL=60° (ΔJKL is an equilateral triangle.)

Then, ∠JKL=∠JKM+∠LKM

Let ∠JKM=∠LKM=x

⇒60°=x+x

⇒2x=60°

⇒x=30°

⇒∠JKM=∠LKM=30°

Therefore in ΔJKM,

∠JKM=30°

∠KJM=60°

∠KMJ=90°

Threfore, ΔJKM is 30-60-90 triangle.

Checking all options,

A. ΔJKM is 45-45-90 triangles. This is incorrect because ∠KJM =60°

B. KM=2JM This option is incorrect as tan60°=√3=KM/JM⇒KM=√3JM

C. JM=KM This option is incorrect as tan60°=√3=KM/JM⇒KM=√3JM

D. ΔJKM is 30-60-90 triangle. This option is correct as in ΔJKM, ∠JKM=30°, ∠KJM=60°, ∠KMJ=90°

Therefore, The correct option is option D: ΔJKM is 30-60-90 triangle.

Learn more about equilateral triangle,

here: https://brainly.com/question/2351368

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