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How can you prove a triangle ABC is isosceles if angle BAD is congruent to angle CAD and line AD is perpendicular to line Bc?
Wiki User
∙ 13y ago
Given: AD perpendicular to BC; angle BAD congruent to CAD
Prove: ABC is isosceles
Plan: Principle a.s.a
Proof:
1. angle BAD congruent to angle CAD (given)
2. Since AD is perpendicular to BC, then the angle BDA is congruent to the angle CDA (all right angles are congruent).
3. AD is congruent to AD (reflexive property)
4. triangle BAD congruent to triangle CAD (principle a.s.a)
5. AB is congruent to AC (corresponding parts of congruent triangles are congruent)
6. triangle ABC is isosceles (it has two congruent sides)
Wiki User
∙ 13y ago
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What does a perpendicular bisector of a triangle split into two congruent parts?
That will depend on what type of triangle it is as for example if it is an isosceles triangle then it will form two congruent right angle triangles.
Angle bisector of angleA of triangleABC is perpendicular to BC prove it is isosceles?
Let D represent the point on BC where the bisector of A intersects BC. Because AD bisects angle A, angle BAD is congruent to CAD. Because AD is perpendicular to BC, angle ADB is congruent to ADC (both are right angles). The line segment is congruent to itself. By angle-side-angle (ASA), we know that triangle ADB is congruent to triangle ADC. Therefore line segment AB is congruent to AC, so triangle ABC is isosceles.
What is a triangle with a right angle and two congruent sides?
A right isosceles triangle.
Can the angle bisector of a triangle also be the perpendicular bisector?
Yes. The bisector of one angle of a triangle is the perpendicular bisector of theopposite side if the bisected angle is the vertex angle of an isosceles triangle,or any angle of an equilateral triangle.
A triangle containing 1 right angle and 2 congruent acute angles is called?
A triangle with 1 right angle and 2 congruent acute angles is both a right triangle and an isosceles triangle.
An angle not congruent to the base angles of an isosceles triangle?
The base angles of an isosceles triangle are congruent. The vertex angle of an isosceles triangle is not necessarily congruent to the base angles.
What does a perpendicular bisector of a triangle split into two congruent parts?
That will depend on what type of triangle it is as for example if it is an isosceles triangle then it will form two congruent right angle triangles.
Angle bisector of angleA of triangleABC is perpendicular to BC prove it is isosceles?
Let D represent the point on BC where the bisector of A intersects BC. Because AD bisects angle A, angle BAD is congruent to CAD. Because AD is perpendicular to BC, angle ADB is congruent to ADC (both are right angles). The line segment is congruent to itself. By angle-side-angle (ASA), we know that triangle ADB is congruent to triangle ADC. Therefore line segment AB is congruent to AC, so triangle ABC is isosceles.
A triangle with two congruent sides and an angle of 104 degrees is?
A triangle with two congruent sides is isosceles. A triangle with an angle of 104 degrees is obtuse. So you would have an obtuse isosceles triangle.
Does the angle bisector of the vertex angle of an isosceles triangle divides the triangle into two congruent?
Only if the vertex angle being bisected is between the sides of equal length will the result be two congruent triangles.
If an angle bisector of an isosceles triangle yields two isosceles triangles what were the angle measures of the original triangle?
they would be congruent triangles!
What is an isosceles obtuse triangle?
An isosceles obtuse triangle is a triangle with 1 obtuse angle and only 2 congruent sides.
What is a triangle with a right angle and two congruent sides?
A right isosceles triangle.
What angle is congruent in an isosceles triangle?
The two "base" angles.
Is a perpendicular bisector always an angle bisector?
thank goodness for my math teacher, norm! he said only in an isosceles triangle. The bisector of the vertex angle of an isosceles triangle is perpendicular to the base! =)
What is the vertex angle on an isosceles triangle?
the top angle the angle formed by the two congruent sides
What do you call a triangle with two congruent sides and an 145 degree angle?
An isosceles triangle
