Adding the Angles in a Triangle

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To Investigate Angle Properties Between Intersecting Lines.

(A). Adjust the sliders to move the triangle around.

What do you find about the angle sum of the angles in a triangle. How do you know?

(B). Interact with the vertices of the triangle in the applet below.

(C). Manipulate the triangle below to verify the conclusion you arrived at in the two activities above.

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To Investigate Angle Properties Between Intersecting Lines.

(A). You are given three angles in the applet below. Can you make a triangle from each set that has these same three angles?

(B). Here is a quadrilateral. Its angles are marked with different colors and are lined up below.

(1). Move the angles to get different quadrilaterals.

(2). What do you notice?

(3). Do you have a conjecture about the angles?

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To Investigate if a Given Set of Angles Form a Triangle.

For the following sets of angles, decide if there is a triangle whose angles have these measures in degrees. Use the closed circle to move the object around, use the opened circle for rotation, and use the square to change the side lengths.

If you get stuck, consider making a line segment. Then use a protractor to measure angles with the first two angle measures.

Is there is a triangle whose angles have the following measures in degrees?

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In a triangle ABC, the measure of angle A is 40°.

(1). Give possible measures for angles B and C if triangle ABC is isosceles.

(2). Give possible measures for angles B and C if triangle ABC is a right-angled.

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Complete the table by drawing a triangle in each cell that has the properties listed for its column and row. If you think you cannot draw a triangle with those properties, write “impossible” in the cell.

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Angle A in triangle ABC is obtuse.

(2). Explain your reasoning.