Isosceles Triangle Theorem Concepts

The video tutorial explains the Isosceles Triangle Theorem, which states that if two sides of a triangle are equal, the angles opposite those sides are also equal. The tutorial guides through the process of proving this theorem using the SAS congruence condition. It involves constructing two triangles by drawing an angle bisector and demonstrating their congruence through the Side-Angle-Side axiom, ultimately proving the theorem.

What does the Isosceles Triangle Theorem state?

• If two sides of a triangle are equal, the angles opposite them are also equal.

• If two angles of a triangle are equal, the sides opposite them are also equal.

• If all sides of a triangle are equal, all angles are also equal.

• If all angles of a triangle are equal, all sides are also equal.

What is the first step in proving the Isosceles Triangle Theorem?

• Measure all angles of the triangle.

• Write down all the given data.

• Construct a perpendicular bisector.

• Draw the triangle and label all sides.

What is the first thing to do before proving something in geometry?

• Construct additional lines.

• Measure all sides.

• Write down all the given data.

• Draw the figure.

What is the purpose of drawing the angle bisector of angle BAC?

• To measure the length of side AD.

• To create two congruent triangles.

• To find the midpoint of side BC.

• To create two right triangles.

What is the measure of angle BAD compared to angle CAD?

• Angle BAD is twice angle CAD.

• Angle BAD is equal to angle CAD.

• Angle BAD is less than angle CAD.

• Angle BAD is greater than angle CAD.

Which segment is common to both triangles ABD and ACD?

• Segment BC

• Segment AD

• Segment AB

• Segment AC

What axiom is used to prove the congruence of triangles ABD and ACD?

• Angle-Angle-Side (AAS)

• Side-Angle-Side (SAS)

• Angle-Side-Angle (ASA)

• Side-Side-Side (SSS)

What can be concluded once triangles ABD and ACD are proven congruent?

• All sides of triangle ABC are equal.

• All angles of triangle ABC are equal.

• Angles ABC and ACB are congruent.

• Sides AB and BC are congruent.

What is the significance of the SAS axiom in this proof?

• It helps in proving the equality of all sides.

• It helps in proving the equality of all angles.

• It helps in proving the congruence of two triangles.

• It helps in finding the length of the sides.

What is the final conclusion of the Isosceles Triangle Theorem proof?

• All angles of the triangle are equal.

• Angles opposite equal sides are equal.

• All sides of the triangle are equal.

• Sides opposite equal angles are equal.