Download Homework Solutions – Section 4.2: pg.178: 1, 3*, 5, 7, 8*, 13

Homework Solutions – Section 4.2: pg.178: 1, 3*, 5, 7, 8*, 13-15
1.
Given: An isosceles triangle and the median to its base
Prove: The median is the perpendicular bisector to the base.
B
Given:
Prove:
A
D
C
3. On problem set
5.
The altitude to a side of a scalene triangle forms two congruent angles with that
side of the triangle.
B
D
Given:
Prove:
A
Statements
1.
2.
3.
4.
Reasons
1. Given
2. An altitude is perpendicular to
the side of a triangle.
3. If two lines are perpendicular,
then they form right angles.
4. If two angles are right then they
are congruent.
C
7.
If the base of an isosceles triangle is extended in both directions, then the exterior
angles formed are congruent.
C
Given:
Prove:
A
Statements
1.
2.
3.
4.
5.
13.
B
E
D
Reasons
1. Given
2. if a triangle is isos, then it has two
congruent sides.
3. If two sides of a triangle are
congruent then the angles opposite
those sides are also congruent.
4. If two angles form a straight angle
then they are supplementary.
5. If two angles are supplementary to
congruent angles then they are
congruent.
If each pair of opposite sides of a four-sided figure are congruent, then the segments
joining opposite vertices bisect each other.
Given:
A
D
Prove:
E
B
C
14.
If a point on the base of an isosceles triangle is equidistant from the midpoints of the
legs, then that point is the midpoint of the base. (equidistant means that if segments
were drawn in then they would be congruent).
C
Given:
Prove:
B
A
15.
D
E
F
If a point in the interior of an angle (between the sides) is equidistant from the sides
of the angle, then the ray joining the vertex of the angle to this point bisects the
angle. (Hint: the distance from a point to a line is defined as the length of the
perpendicular segment from the point to the line).
C
Given:
⃗⃗⃗⃗⃗ ,
⃗⃗⃗⃗⃗
B
Prove: ⃗⃗⃗⃗⃗
D
F
A
G
E