Illustrative Mathematics - Geometry - Mathematics - Unit 2 - Lesson 10

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8 Questions

Painters and carpenters use scaffolding to climb buildings from the outside. What shapes do you see? Why does one figure have more right angles?

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Select all true statements based on the diagram.

Angle CEB is congruent to angle DEA.

Angle CBE is congruent to angle ABE.

Line DA is parallel to line CB.

Segment DA is congruent to segment CB.

Line DC is parallel to line AB.

Segment DC is congruent to segment AB.

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Prove ABCD is a parallelogram.

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Tyler has proven that triangle WYZ is congruent to triangle WYX using the Side-Side-Side Triangle Congruence Theorem. Why can he now conclude that diagonal WY bisects angles ZWX and ZYX?

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WXYZ is a kite. Angle WXY has a measure of 133 degrees and angle ZYX has a measure of 34 degrees. Find the measure of angle ZWY.

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Elena is thinking through a proof using a reflection to show that the base angles of an isosceles triangle are congruent. Complete the missing information for her proof.
Call the midpoint of segment  CD ___1___. Construct the perpendicular bisector of segment CD. The perpendicular bisector of CD must go through B since it's the midpoint. A is also on the perpendicular of CD because the distance from A to ___2___ is the same as the distance from A to ___3___. We want to show triangle ADC is congruent to triangle ACD. Reflect triangle ADC across line ___4___. Since ___5___ is on the line of reflection, it definitely lines up with itself. DB is congruent to ___6___ since AB is the perpendicular bisector of CD. D' will coincide with ___7___ since it is on the other side of a perpendicular line and the same distance from it (and that’s the definition of reflection!). C' will coincide with ___8___ 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 ADC onto triangle ACD, that means angle ___9___ will be taken onto angle ___10___ (they are corresponding parts under the same reflection), and therefore they are congruent.

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Segment EG is an angle bisector of angle FGH. Noah wrote a proof to show that triangle HEG is congruent to triangle FEG. Noah's proof is not correct. Why is Noah's proof incorrect?
Side EG is congruent to side EG because they're the same segment.
Angle EGH is congruent to angle EGF because segment EG is an angle bisector of angle FGH.
Angle HEG is congruent to angle FEG because segment EG is an angle bisector of angle FGH.
By the Angle-Side-Angle Triangle Congruence Theorem, triangle HEG is congruent to triangle FEG.

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

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This lesson is from Illustrative Mathematics. Geometry, Unit 2, Lesson 10. Internet. Available from https://curriculum.illustrativemathematics.org/HS/teachers/2/2/10/index.html ; accessed 29/July/2021.

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