Understanding Angle Bisectors in Triangles

This video tutorial explains how to construct the angle bisectors of a triangle using a compass and straight edge. It covers the process for each vertex, demonstrating how to create congruent angles by bisecting the interior angles. The tutorial also discusses the point of concurrency, known as the incenter, which is equidistant from the triangle's sides. The video concludes with the concurrency of angle bisector theorem, stating that the angle bisectors intersect at a point equidistant from the triangle's sides.

What tools are necessary to construct the angle bisectors of a triangle?

• Compass and straight edge

• Ruler and pencil

• Protractor and ruler

• Calculator and pencil

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What is the first step in constructing the angle bisector for angle A?

• Draw a circle around the triangle

• Measure the angle with a protractor

• Place the compass at vertex A and swing an arc

• Draw a straight line

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After swinging the first arc at vertex A, what should you do next?

• Swing another arc at vertex B

• Change the radius of the compass

• Draw a line through the arc

• Measure the arc length

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CCSS.HSG.CO.B.6

What is the result of bisecting angle A?

• A right angle

• Two congruent angles

• An obtuse angle

• Two unequal angles

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CCSS.HSG.CO.C.9

How do you ensure the angle bisector for angle B is accurate?

• Draw a circle around the angle

• Use a ruler to draw the bisector

• Measure the angle with a protractor

• Swing arcs from both intersection points

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What is the significance of the point where angle bisectors intersect?

• It is the centroid

• It is the orthocenter

• It is the incenter

• It is the circumcenter

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What property does the incenter have regarding the sides of the triangle?

• It is the shortest distance from the vertices

• It is equidistant from the vertices

• It is equidistant from the sides

• It is the longest distance from the sides

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CCSS.HSG.C.A.3

What can be constructed using the incenter of a triangle?

• A square

• A rectangle

• A tangent line

• An inscribed circle

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CCSS.HSG.C.A.3

What does the concurrency of angle bisectors theorem state?

• Angle bisectors form a right angle

• Angle bisectors intersect at a point equidistant from the sides

• Angle bisectors intersect at the centroid

• Angle bisectors are parallel

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CCSS.HSG.C.A.3

What is the relationship between the incenter and the inscribed circle?

• The incenter is on the circle

• The incenter is the center of the circle

• The incenter is outside the circle

• The incenter is tangent to the circle

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