SOLUTION: the midpoint of the hypotnuse of a right triangle is equidistant from the vertices. given: angle MON is a right angle, P is the midpoint of MN Prove: MP= PN =OP

Question 31474This question is from textbook new york math a/b
: the midpoint of the hypotnuse of a right triangle is equidistant from the vertices.
given: angle MON is a right angle, P is the midpoint of MN
Prove: MP= PN =OP This question is from textbook new york math a/b

Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
the midpoint of the hypotnuse of a right triangle is equidistant from the vertices.
WHAT IS THE TRIANGLE NAME?MNO?
given: angle MON is a right angle,
OK...ASSUMING MNO IS THE TRIANGLE
MN IS HYPOTENUSE.
P is the midpoint of MN
SO MP=PN.
NOW IF WE TAKE MN AS DIAMETER AND P ITS MIDPOINT AS CENTRE AND DRAW A CIRCLE
IT SHOULD PASS THROUGH O,SINCE ANGLE MON=90 AS GIVEN AND A SEMICIRCLE SUBTENDS 90 ANGLE AT ANY POINT ON ITS CIRCUMFERENCE AND VISE VERSA.AS O LIES ON CIRCLE AND PI NTHE CENTRE PO=RADIUS = DIAMETER/2=MN/2=MP=PN AS P IS MIDPOINT OF MN.
Prove: MP= PN =OP
MN IS

Prove: MP= PN =OP
RELATED QUESTIONS
The midpoint of the hypotenuse of a right triangle is equidistant frorm the 3... (answered by MathLover1,ikleyn)

prove that the midpoint of the hypotenuse of a right triangle is equidistant from the... (answered by ikleyn)

If the vertices of the right angle triamgle ABC are A(-1,2) B(3,8) C(5,-2) use coordinate (answered by Alan3354)

Show algebraically that this triangle is a right triangle. The triangle has the vertices... (answered by Alan3354,KMST,ikleyn)

Writing to Learn Equidistant Point from Vertices of a Right Triangle Prove that the... (answered by stanbon,ikleyn)

Prove: The midpoint of the hypotenuse of a right triangle is equidistant from the three... (answered by richard1234)

prove that in a right triangle the mid point of hypotenuse is equidistant from all the... (answered by ikleyn)

Given: 0 is the midpoint of line segment MQ. 0 is the midpoint of line segment... (answered by richwmiller)

If I have a right triangle with legs 6 inches and 8 inches long. How far is the midpoint (answered by Fombitz)