EOC Review #5Thursday

1. Given: Endpoint (2, 3); Midpoint (3, -4)Find the missing endpoint.

EOC REVIEW QUIZ TOMORROW

Honors H.W. #23pg. 246

#2-32 and 38 (even)

H.W. QUESTIONS?

38.) In GHJ, K(2,3) is the midpoint of GH, L(4,1) is the midpoint of HJ, and M(6,2) is the

midpoint of GJ.

Bisectors in TrianglesToolkit #5.2

Today’s Goal:1. To use properties of

perpendicular bisectors and angle bisectors.

Perpendicular Bisector: equidistant from the endpoints of a segment (cuts SEGMENT in two EQUAL parts), and makes a RIGHT ANGLE with that segment.

When three perpendicular bisectors meet, that POINT is called the CIRCUMCENTER.

Find the set of points on the map of D.C. that are equidistant from the Jefferson Memorial and the White House.

Ex.1: CD is the perpendicular bisector of

AB. Find CA and DB.

Angle Bisector: equidistant from the sides of a triangle – cuts an ANGLE into TWO EQUAL parts.

When three angle bisectors meet, the POINT is called the INCENTER.

Ex.2(a): Find the value of x, then find FD and FB.

Ex.2(b): Check Understanding

a) According to the diagram,

how far is K from EH? From

ED?

b) What can you conclude

about EK?

c) Find the value of x.

d) Find mDEH.

In-Class Practice (Part I)Geometry Book

Pg. 251 #’s 1-4, 6-11

Solutions – Part I

1. AC is the bis. of BD

2. 15

3. 18

4. 8

6. x = 12, JK = JM = 17

7. y = 3, ST = TU = 15

8. HL is the bis. of

JHG.

9. y = 9, mFHL=54,

mKHL=54

10. 27

11. Point E is on the

bisector of KHF.

In-Class Practice (Part II)Geometry Book

Pg. 252 #’s 12-15, 18-25

Solutions – Part II

12. 513. 1014. 1015. Isoscele

s

18. 1219. 420. 421. 1622. 523. 1024. 725. 14

In-Class Practice (Part III)Geometry Book

Pg. 252 #’s 28-30

(Draw picture!)

Solutions – Part III

28. No, A is not equidistant

from the sides of X

29. Yes, AX bisects TXR

30. Yes, A is equidistant

from the side of X.

pg. 253#40

Bisectors & GraphingCh. 5.2 Extension

Today’s Goal(s)1. To investigate perpendicular and

angle bisectors on the coordinate plane.

Example:Given points A(1,3), B(5,1), and C(4,4), does C lie on the bisector of AB?

Plot points first!

Then determine whether AC = BC.

#5 Perpendicular Bisectora. (-2,7) b. (-1,6) c. (0,5)

#6 Angle Bisectora. (6,5) b. (7,8) c. (4,4)

You are given the points A(4, 8), O(0,0), and B(12, 0).

What did the waiter say when he delivered the potato?

What was Humpty-Dumpty’sCause of death?

Concurrent Lines, Medians, and

AltitudesToolkit 5.3

Today’s Goal:1. To identify properties of

medians and altitudes of a triangle.

STOP and THINK!What does concurrent mean?

When three or more lines intersect in one point, the point at which they intersect is the point of concurrency.

Median of a triangle: a segment that connects a VERTEX to the MIDPOINT of the opposite side.

When three medians meet, the POINT is called the CENTROID.

The medians of a triangle are concurrent at a point where the distance from the point to the vertex is TWICE the distance from the point to the side.

Ex.1(a): Finding Lengths of Medians

D is the centroid of ABC and DE = 6. Find BE.

Ex.1(b): Finding Lengths of Medians

You Try…

M is the centroid of WDR, and WM = 16.

Find WX.

Altitude of a triangle: a segment that is PERPENDICULAR to a side, and connects a VERTEX to the opposite side.

When three altitudes meet, the POINT is called the ORTHOCENTER.

4 Points of Concurrency Summary

Helpful Hint!

CM PBIN ABC

MO A

Other Uses!Perpendicular Bisectors

Pt. of Concurrency:

The circle is circumscribedabout ABC.

Other Uses!Angle Bisectors

Pt. of Concurrency:

The circle is inscribedin ABC.

Other Uses!Medians

Pt. of Concurrency:

“Balance Point”Also called the center of gravity of a triangle because it is the point where a triangular shape will balance.

Other Uses!Altitudes

Pt. of Concurrency:

“Heights” of a triangle.

Ex.2(a.): Find the center of the circle that circumscribes XYZ.

Ex.2(b.): Find the center of the circle that circumscribes XYZ.

X(0,0), Y(0,6), Z(4,0)

You Try…