AA Similarity Exploration

Please use this to investigate AA Similarity for triangles.

[size=150][color=#0000ff]In the applet above use the [/color][color=#ff0000]red[/color][color=#0000ff] and [/color][color=#38761d]green[/color][color=#0000ff] sliders on the right of the screen to change the angle measures. The slider will change the angles in both triangles.[/color][/size]

As you change the sliders for the angle measures observe the ratios of the corresponding sides. Which of the following can you say is true for any angle measure?

The ratios of all three corresponding sides stays the same, as long as the triangles are obtuse. The ratios of all three corresponding sides stays the same, as long as the triangles are right triangles. The ratios of all three corresponding sides always stays the same. The ratios of all three corresponding sides stays the same, as long as the triangles are acute.

[color=#9900ff]In the applet above click and drag the [/color][color=#0000ff]blue[/color][color=#9900ff] vertices ([/color][math]\angle A[/math][color=#9900ff], [/color][math]\angle B[/math][color=#9900ff], [/color][math]\angle D[/math][color=#9900ff], and [/color][math]\angle F[/math][color=#9900ff]). [/color]

As you move the vertices, which of the following are true?

The angle measures change. The lengths of the sides change, but the ratio of the corresponding sides remains proportionate. The angle measures do not change. The lengths of the sides change, causing the ratios of corresponding sides to not be proportionate.

[color=#ff7700]Use your answers from the previous two questions (and explore the applet more) to answer the following question.[/color]

What can be said about two triangles that have two congruent corresponding angles?

The triangles are congruent because the corresponding parts are congruent. Only obtuse triangles with two congruent angles are similar. The triangles are similar, because the corresponding sides are proportionate. Only acute triangles with two congruent angles are similar. Only right triangles with two congruent angles are similar.

AA Similarity Exploration

Information: AA Similarity Exploration