nm standards: afg.c.5, gt.a.5, gt.b.4, dap.b.3

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NM Standards: AFG.C.5, GT.A.5, GT.B.4, DAP.B.3

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NM Standards: AFG.C.5, GT.A.5, GT.B.4, DAP.B.3. Any point that is on the perpendicular bisector of a segment is equidistant from the endpoints of the segment. M. B. N. B. M. P. D. If is an angle bisector, then PM = PN. P. A. C. N. D. A. C. - PowerPoint PPT Presentation

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Page 1: NM Standards: AFG.C.5, GT.A.5, GT.B.4, DAP.B.3

NM Standards: AFG.C.5, GT.A.5, GT.B.4, DAP.B.3

Page 2: NM Standards: AFG.C.5, GT.A.5, GT.B.4, DAP.B.3

Any point that is on the perpendicular bisector of a segment is equidistant from the endpoints of the segment.

Any point equidistant from the endpoints of a segment lies on the perpendicular bisector of the segment.

Any point on the angle bisector is equidistant from the sides of the angle.

Remember, distance is always measured on the perpendicular.

Any point equidistant from the sides of an angle lies on the angle bisector.

If PM = PN, then is an angle bisector.

AD

M

NA C

B

P

D

M

NA C

B

P DIf is an angle bisector,

then PM = PN

AD )( DACBAD

Page 3: NM Standards: AFG.C.5, GT.A.5, GT.B.4, DAP.B.3

DefinitionsDefinitionsPoint of Concurrency -

A common point in which three or more lines intersect

Circumcenter -The intersection point of the three perpendicular bisectors of a triangle

Incenter -The intersection point of the three angle bisectors of a triangle

Centroid -The intersection point of the three medians of a triangle

Orthocenter -The intersection point of the three altitudes of a triangle

Page 4: NM Standards: AFG.C.5, GT.A.5, GT.B.4, DAP.B.3

TheoremsTheorems

Circumcenter Theorem-The circumcenter of a triangle is equidistant from the vertices of the triangle

Incenter Theorem-

The incenter of a triangle is equidistant from each side of the triangle

Centroid Theorem-

The centroid of a triangle is two-thirds the distance of its corresponding median of the triangle

Page 5: NM Standards: AFG.C.5, GT.A.5, GT.B.4, DAP.B.3

ALGEBRA Points U, V, and W are the midpoints of respectively. Find a, b, and c.

Find a.

Segment Addition Postulate

Centroid Theorem

Substitution

Multiply each side by 3 and simplify.

Subtract 14.8 from each side.

Divide each side by 4.

Page 6: NM Standards: AFG.C.5, GT.A.5, GT.B.4, DAP.B.3

Find b.Segment Add Postulate

Centroid Theorem

Find c.

Segment Addition Postulate

Centroid Theorem

Page 7: NM Standards: AFG.C.5, GT.A.5, GT.B.4, DAP.B.3

ALGEBRA Points T, H, and G are the midpoints of respectively. Find w, x, and y.

Answer:

Page 8: NM Standards: AFG.C.5, GT.A.5, GT.B.4, DAP.B.3

HW : Page 242HW : Page 242

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