In triangle PQR, <p = 30 degrees

<Q = 80 degrees

<R = 70 degreees

QH is an altitude and RM is a median and H is on the line PR,

the measure of <MHP is:

a) 15 degrees or 20 degrees or 30 degrees or 40 degrees or 45 degreess ?

diagram is attatched

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- May 25th 2009, 01:58 PMforeverbrokenpromisesTriangle PQR...
In triangle PQR, <p = 30 degrees

<Q = 80 degrees

<R = 70 degreees

QH is an altitude and RM is a median and H is on the line PR,

the measure of <MHP is:

a) 15 degrees or 20 degrees or 30 degrees or 40 degrees or 45 degreess ?

diagram is attatched - May 25th 2009, 05:49 PMI-Think
Multiple hellos. It is 30 degrees.

Solution: (All angular measurements in degrees)

degrees

degrees

degrees

is an altitude and is a median and is on the line

If is an altitude, then and are .

Filling in relevant angles angles: ,

Area of

A median splits a triangle into two triangles equal in area.

Construct altitude . (dotted line in diagram, forgot to label O)

Two similar triangles are discovered, and (as and are parallel)

Calculate area of

(Because a median splits a triangle into two triangles equal in area.)

Hence,

Which means that and

Thus

Hence and are identical

Hence