NAME ______Median Altitude #7

1.   Find the following lengths:

a.   BE = ______

b.   DE =______EF= ______DF= ______

Because ______

c.   TE = ______BT = ______

d.   AT = ______TD = ______AD = ______

2. Using the information from question #1, find the following.

a.  In DABC , let AH be the altitude from the vertex A to side BC. Find …

AH = ______BH = ______

b.  How long is EH ? ______

c.  What is the area of DABT ? ______

d.  How far is T from AB ? ______

e.  What is the perimeter of D EFH ? ______

3.  Refer to problem #1 to find the following areas:

a.   D ABC = ______D DEF = ______

b.   D BED = ______D ATB = ______

c.   D DFT = ______D CDT = ______

d.   Area of quadrilateral DEFT = ______

e.   Area of pentagon AFTDC = ______

4.  Find the following based on the triangle at right, with the angle bisectors as indicated.

a.  Find BE = ______

b. 

b. BD =______DC= ______

c. Find PE = ______BP = ______

d. If circle P intersects AB at point W, AB = BC = 45, AC = 72 find BW = ______and AW = _____

e. How far is point P from AB ?

f.   What is the radius of the circle inscribed in DABC ?

Fill in the blanks below to complete the theorems:

5. The ______of a right triangle meet at a vertex of the triangle.

6. A Euler line contains the three points where the ______, ______, and ______meet.

7.  An angle bisector separates the opposite side of the triangle into two segments ______

______.

8.  The radius of an circumscribed circle of a right triangle is always ______.

9.  The radius of an inscribed circle can be found by using the formula ______.

10.  Any point on an ______is equidistant to its sides.

11.  The median to the hypotenuse of any right triangle is always ______.

12.  The ______, ______, and ______are the same segment if the triangle is ______and the segments are drawn to the ______.

13.  The midpoint of the hypotenuse of a right triangle is where the ______meet.

14.  The ______meet outside a triangle if the triangle is ______.

15.  The medians to the legs of an isosceles triangle are ______.

16.  The ______meet at the center of the inscribed circle.

17.  The ______meet at the center of the circumscribed circle.

18.  The most important theorem about altitudes is that ______.

19.  An equilateral triangle is very special since all three medians are congruent, and each is also the ______, ______, and part of the ______.

20.  The angle bisector of a triangle separates the side to which it is drawn into two segments whose ratio ______.

Geometry Honors Livingston High School Mr. Lamb, Mr. Memory

Median Altitude #7 Mathematics Department