IM Geo.2.9 Lesson: Side-Side-Side Triangle Congruence

Construct a triangle with the given side lengths using the applet below.[br]Side lengths:[br][list][*]2 cm[/*][*]1.5 cm [/*][*]2.4 cm[/*][/list]Can you make a triangle that doesn’t look like anyone else’s?
Priya was given this task to complete:
Use a sequence of rigid motions to take STU onto GHJ. Given that segment ST is congruent to segment GH, segment TU is congruent to segment HJ, and segment SU is congruent to segment GJ. For each step, explain how you know that one or more vertices will line up.[br][img]data:image/png;base64,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[/img]
Help her finish the missing steps in her proof:
[img]data:image/png;base64,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[/img][br]Now, help Priya by finishing a few-sentence summary of her proof. “To prove 2 triangles must be congruent if all 3 pairs of corresponding sides are congruent . . . .”
It follows from the Side-Side-Side Triangle Congruence Theorem that, if the lengths of 3 sides of a triangle are known, then the measures of all the angles must also be determined. Suppose a triangle has two sides of length 4 cm.
Use a ruler and protractor to make triangles and find the measure of the angle between those sides if the third side has these other measurements.
Do the side length and angle measures exhibit a linear relationship?
Quadrilateral ABCD is a parallelogram.
 By definition, that means that segment [math]AB[/math] is parallel to segment [math]CD[/math], and segment [math]BC[/math] is parallel to segment [math]AD[/math].[br][br]Prove that angle [math]B[/math] is congruent to angle [math]D[/math].
Work on your own to make a diagram and write a rough draft of a proof.
With your partner, discuss each other’s drafts.
[list][*]What do you notice your partner understands about the problem?[/*][/list]
[list][*]What revision would help them move forward?[/*][/list]
Work together to revise your drafts into a clear proof that everyone in your class could follow and agree with.

IM Geo.2.9 Practice: Side-Side-Side Triangle Congruence

A kite is a quadrilateral which has 2 sides next to each other that are congruent and where the other 2 sides are also congruent.
Given kite [math]WXYZ[/math], show that at least one of the diagonals of a kite decomposes the kite into 2 congruent triangles.
Mai has proven that triangle WYZ is congruent to triangle WYX using the Side-Side-Side Triangle Congruence Theorem.
Why can she now conclude that diagonal [math]WY[/math] bisects angles [math]ZWX[/math] and [math]ZYX[/math]?
WXYZ is a kite.
Angle [math]WXY[/math] has a measure of 133 degrees and angle [math]ZWX[/math] has a measure of 60 degrees. Find the measure of angle [math]ZYW[/math].
Each statement is always true.
Select [b]all[/b] statements for which the converse is also always true.
Prove triangle [math]ABD[/math] is congruent to triangle [math]CDB[/math].
Triangles ACD and BCD are isosceles.
[size=150]Angle [math]DBC[/math] has a measure of 84 degrees and angle [math]BDA[/math] has a measure of 24 degrees. [/size][br]Find the measure of angle [math]BAC[/math].
Reflect right triangle ABC across line AB.
Classify triangle [math]CAC'[/math] according to its side lengths. Explain how you know.

Information