IM Geo.2.10 Practice: Practicing Proofs

Why does one figure have more right angles?

Select all true statements based on the diagram.

Why can he now conclude that diagonal  bisects angles  and ?

Angle  has a measure of 133 degrees and angle  has a measure of 34 degrees. Find the measure of angle .

Complete the missing information for her proof.  Call the midpoint of segment  . Construct the perpendicular bisector of segment . The perpendicular bisector of  must go through since it's the midpoint.  is also on the perpendicular of  because the distance from  to  is the same as the distance from  to . We want to show triangle  is congruent to triangle . Reflect triangle  across line . Since  is on the line of reflection, it definitely lines up with itself.  is congruent to  since  is the perpendicular bisector of .  will coincide with  since it is on the other side of a perpendicular line and the same distance from it (and that’s the definition of reflection!).  will coincide with  since it is on the other side of a perpendicular line and the same distance from it (and that’s the definition of reflection!). Since the rigid transformation will take triangle onto triangle ,that means angle  will be taken onto angle  (they are corresponding parts under the same reflection), and therefore they are congruent.

Noah wrote a proof to show that triangle is congruent to triangle .

• Side  is congruent to side  because they're the same segment.
• Angle  is congruent to angle  because segment  is an angle bisector of angle .
• Angle  is congruent to angle  because segment  is an angle bisector of angle .
• By the Angle-Side-Angle Triangle Congruence Theorem, triangle  is congruent to triangle .

Draw an auxiliary line in figure  to create a quadrilateral. Draw the image of the auxiliary line when rotated 90 degrees counterclockwise around point .  Write a congruence statement for the quadrilateral you created in figure  and the image of the quadrilateral in figure .