Show that triangle mpt =triangle mtp

Unusual notation.  I won't fuss with it.

a. We have isosceles PRT, so angle  RPT = angle RTP.

By the definition of angle bisector, angle MTP = angle MTF, and angle MPT = angle MPU.

We have m angle RTP = m angle MTF + m angle MTP = 2 m angle MTP

Similarly, m angle RPT = 2 m angle MPT

2 m angle MTP = 2 m angle MPT

angle MPT = angle MPT

That's the first part.

b. That makes MPT isosceles.

c. 2x+124=180

2x = 56

x = 28 degrees

MTP = 28 degrees

d.  We have angle RPT=angle RTP=56 so PRT=180-2(56)=68 degrees

PUT = 180 - UTP - UPT = 180 - 28 - 56 = 96 degrees

Bad drawing, PUT looks acute.

angle PRT = 68 degrees, angle PUT = 96 degrees

answer: download photomath it's legit.

step-by-step explanation:

c. y = 1/4 x + 5

step-by-step explanation:

first, put the equation of the line on the graph into slope-intercept form

(y = mx + b):   y = -4x + 8

second, a perpendicular line has to have "an opposite/reciprocal slope" to the original slope. so, find the "m" value in your original equation (it's -4, right? )

original slope: m = -4   perpendicular slope: change the sign to its opposite and find the reciprocal ("flip" the number)

new slope is now positive (b/c the original slope was negative 4), and it's 1/4 (not the original slope of 4 or 4/1)