Ch 5 more practice answers
1. Every point on the perpendicular bisector of a segment is equidistant from the endpoints of the
segment.
2. The construction of a perpendicular bisector locates two points equidistant from the endpoints of the
segment. Since two point determine a line, these points determine the perpendicular bisector.
3. Every point on an angle bisector is equidistant from the sides of the angle.
4. The construction of an angle bisector locates two points on the sides of the angle that are equidistant
from the vertex of the angle. The construction continues by finding another point that is equidistant
from those two points. Thus this construction creates the perpendicular bisector of the base of an
isosceles triangle which is also the angle bisector of the vertex angle.
5. Use the coordinates of two points to find the coordinates of the midpoint of that side by averaging
the x and y coordinates of the endpoints to get the x and y coordinates of the midpoints. Use the
coordinates of the midpoint and the coordinates of the third vertex to find the slope of the median.
Then use either of these two points and the slope to write the equation of the line containing the
median.
6. Use the coordinates of two points to find the slope of that side. The slope of the altitude to that side
will be the opposite reciprocal of that first slope. Then use the third vertex and the slope of the
perpendicular to the side to write the equation of the altitude.
7. The orthocenter where the lines containing the altitudes meet has no other special property.
9. The incenter (angle bisectors) and centroid (medians) must be inside the triangle. The circumcenter
(perpendicular bisectors) meet inside an acute triangle, outside an obtuse triangle and at the midpoint
of the hypotenuse of a right triangle. In orthocenter is inside an acute triangle, outside an obtuse
triangle and at the right angle vertex of a right triangle.
10. The smallest side of a triangle is opposite the smallest angle of the triangle.
11. You can compare the sides of two different triangles if you know the other two pairs of
corresponding sides are congruent AND if you know the measures of the angles included by those sides.
12. The measure of an exterior angle of an acute triangle will be greater than all the interior angle
measures. The exterior angle of a right or obtuse triangle will always be greater than the measures of
the remote interior angles and will sometimes be greater than it’s adjacent supplement.
H
13.
1. HG || EF , HE || GF , EF  FG
1. Given
G
2
1
F
2. 2  GEF , 1  EGF
3. m2=mGEF , m1  mEGF
2. Alternate interior angles from by parallel lines and a transversal are congruent.
3. Def. of congruent angles
4. mEGF  mEFG
4. In a triangle, the larger angle is opposite the longer side.
5. m1 > m2
E
5. Substitution
S
14.
1. TU  US  SV
2. V  SUV
3. mV  mSUV
4. mSUV  mT
5. mV  mT
6. ST  SV
V
U
T
1. Given
2. In a triangle angles opposite congruent sides are congruent.
3. Def. of congruent angles
4. The measure of the exterior angle of a triangle is greater than the measures of
the remote interior angles.
5. Substitution
6. In a triangle the longer side is opposite the larger angle.