Question

9 practice 9 (from unit 2, lesson 14)
select all statements that must be true.
a the angle bisector of an isosceles triangle is also the perpendicular bisector.
b the angle bisector of any angle divides the angle into 2 congruent parts.
c the median of a triangle is also the perpendicular bisector.
d the median of an isosceles triangles is also the angle bisector.
e the median of a triangle is also the angle bisector.
how did i do?

Explanation:

• Option A: Only the angle bisector of the vertex angle in an isosceles triangle is a perpendicular bisector; this is not true for base angles, so it is not always true.
• Option B: By definition, an angle bisector splits an angle into two congruent (equal-measure) angles, so this is always true.
• Option C: A median only acts as a perpendicular bisector in isosceles/equilateral triangles, not all triangles, so it is not always true.
• Option D: In an isosceles triangle, the median drawn from the vertex angle (between the two equal sides) is also the angle bisector (and perpendicular bisector) due to the triangle's symmetry, so this is always true.
• Option E: A median is only an angle bisector in isosceles/equilateral triangles, not all triangles, so it is not always true.

Answer:

B. The angle bisector of any angle divides the angle into 2 congruent parts.
D. The median of an isosceles triangles is also the angle bisector.