Question

Determine if each statement is true or false.

Triangle L M N. Angle N is thirty degrees. From M, segment M P is drawn such that P is on side L N and M P forms a right angle with side L N. Angle L M P is thirty degrees.


A ∆LPM is similar to ∆LMN.
True False

B ∆LPM is similar to ∆MPN.
True False

C ∆MPN is similar to ∆LMN.
True False

D ∆MPN is similar to ∆LPM.
True False

Answer 1

m∠L + m∠M = 90°

sin(L) = 0.66913

sin(M) = 0.74314

Explanation:

The sum of the two angles is ...

m∠L + m∠M = 42° +48° = 90°

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A calculator can show you the sines of these angles.

sin(42°) ≈ 0.66913

sin(48°) ≈ 0.74314

_____

The two acute angles of a right triangle always have a sum of 90°.

Answer 2

its all true

Explanation:

A B C D are true