IM Geo.2.15 Practice: Congruence for Quadrilaterals

Select all quadrilaterals that have 180 degree rotational symmetry.

square isosceles trapezoid parallelogram rectangle rhombus trapezoid

Lin wrote a proof to show that diagonal EG is a line of symmetry for rhombus EFGH. Fill in the blanks to complete her proof.

Because [math]EFGH[/math] is a rhombus, the distance from [math]E[/math] to [img]data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAHIAAAAVCAYAAACaLLqfAAABQElEQVRoBe2YPQqEQAyF5xieY7G3thFsLfQGtoKgHsDG3s7KP7Cz0Wt4Fm00SxYGbMx2woQEHoaJxeR9o46jQIKFA4pFF0QT13VBlmVQFAVxl/klliA1vDAM4fP5gFIK8jw3nxbRAWuQCM+yLAFJLABjSrZtC0hjaBET9X1fQBL+GFOK41hAGkOLmGhZlgKS8MeYUl3XP5D4C8I5WO5a78CappEn8m6IqXnbtgLSVHj3eU/TJCDvhpiaz/MsIE2Fh0d067r+pF+teNaKY8uyANa5BcvNDoJyHOdR53ly4wgsQSIlhKmF4HSOV47BFiRHWFRP6r5Sn/J93wF1HIfoZQ+0909s9LhKkgTSNCXleR64rgt4AC1614MgCCCKIpIP8lPbtsE/VVUFfd/DOI6ilz3oug6GYfjLSL6R1IfHoNoXCHKP6iwprOEAAAAASUVORK5CYII=[/img] is the same as the distance from [math]E[/math] to [img]data:image/png;base64,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[/img]. Since [math]E[/math] is the same distance from [img]data:image/png;base64,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[/img] as it is from [img]data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAHIAAAAZCAYAAADt7nrkAAABjElEQVRoBe2YP8+CMBDG+8nEuLGIfzYXvgYxQGJYGDRx8zMgjEzIyOTgBl9FE5HnzZHUOLwSJ5Oe1+QJtDD07tfr9aogjYUHFAsrxAj8BMiu6/B4PFjj/gmQTdNAKYW2bdnCZA+SInGxWAhIk5cwbanb7Rbj8VhAmgyyqiosl0uMRiMBaSrI+/2OyWSCy+UCy7IEpKkgoyjCbrfrT6sC0lCK5/MZjuPgdruB8qSANBAkgZvNZsjzvJ+9gDQQIk35cDjA87w+EqkvIA0ESQU/nVCp5KD8GMcxNpvNc2sNggAkjrc8rC4ECBCBCsPwKerrHCkgDYxOPWWCq+tIKkm4NlYR+QqJcmNZljidTs+ILIqiH6Nv3BprkLSl/ifJkYYtY4o8LYKn3w0z46Ppso3Ij6xn9JPSq/Td83q9gkS3JKLv+kD7/h2b13G1Xq8xpOl0Ctu2MZ/PRV/2wWq1guu6g3yIne/7UHVdY0j7/R7H4xFZlom+7IMkSZCm6SAfzU5yJJM8KSAFJBMPMDHjD/y7k0BjMXOvAAAAAElFTkSuQmCC[/img], it must lie on the perpendicular bisector of segment [img]data:image/png;base64,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[/img]. By the same reasoning, [math]G[/math] must lie on the perpendicular bisector of [img]data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAHIAAAAYCAYAAAAmsqlBAAACCUlEQVRoBe2Yv+tBURjGz26WQvJPGCwokcViMmGhlCLdQYndbOKvICVkoYzKbqHYLSx+PN/eU0f3fodbd5H7Om+9de8999Z5n0/PPe85AjpYKCBYVKGLwM+AfL1erHGzBUngdrsd2u02EokECoUCTqcTW5gsQRLE+XyOUCiETqeD4/GIxWKBcrmM5/PJEiZLkJvNBkIIrFYrCY3ghcNheL1ePB4PDdINChC0fD6PYDD4dh85tFQqyd8r17WSnSNns5l0YzKZlCAJrEquEMlg7ED2+30JMpfLyTWRGp1oNIput/t2qBv+LE7nyAokOa5Wq0mQlUoF6/Ua9Gw6ncLv96PX68l7pyK54X12IOPxuAQZiUQsjQ05khqg8/nsBi6O58gOpHIkgTOHAknu5BisQBKgwWAgnUf7R3MokP8Bm99x8zU7kNvtVoIsFosWLhqkRY7vv7nf7wgEAshkMpbGhkB6PB55bPf9VTifITtH0p6x2WxKV9IJj7lrbbVaFrjO5freL9iBJKnpGK5arcLn80F1sfV6nS1EqpklSCqMnHm5XLBcLnE4HFgfBrAGScX9UrB15C9BpFrFfr+HXQ6HQ4zHY0wmE50f1mA0GoHSjo8aE4ZhwC7T6TRSqRSy2azOD2sQi8VA+2E7PjTWaDQgqD23y+v1Csrb7abzwxoo7e34qDG9RjJZTP8AMCe3WgAMiOIAAAAASUVORK5CYII=[/img]. Therefore, line [img]data:image/png;base64,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[/img] is the perpendicular bisector of segment [math]FH[/math]. So reflecting rhombus [math]EFGH[/math] across line [img]data:image/png;base64,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[/img] will take [math]E[/math] to [img]data:image/png;base64,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[/img] and [math]G[/math] to [img]data:image/png;base64,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[/img] (because [math]E[/math] and [math]G[/math] are on the line of reflection) and [math]F[/math] to[img]data:image/png;base64,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[/img] and [math]H[/math] to [img]data:image/png;base64,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[/img] (since [math]FH[/math] is perpendicular to the line of reflection, and [math]F[/math] and [math]H[/math] are the same distance from the line of reflection, on opposite sides). Since the image of rhombus [math]EFGH[/math] reflected across [math]EG[/math] is rhombus [math]EHGF[/math] (the same rhombus!), line [math]EG[/math] must be a line of symmetry for rhombus [math]EFGH[/math].

In quadrilateral ABCD, AD is congruent to BC, and AD is parallel to BC.

Andre has written a proof to show that ABCD is a parallelogram.

[size=150]Fill in the blanks to complete the proof. [/size][br][br]Since [math]AD[/math] is parallel to [img]data:image/png;base64,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[/img], alternate interior angles [img]data:image/png;base64,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[/img] and [img]data:image/png;base64,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[/img] are congruent. [math]AC[/math] is congruent to [img]data:image/png;base64,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[/img] since segments are congruent to themselves. Along with the given information that [math]AD[/math] is congruent to [math]BC[/math], triangle [math]ADC[/math] is congruent to[img]data:image/png;base64,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[/img] by the [img]data:image/png;base64,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[/img] Triangle Congruence. Since the triangles are congruent, all pairs of corresponding angles are congruent, so angle [math]DCA[/math] is congruent to [img]data:image/png;base64,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[/img]. Since those alternate interior angles are congruent, [math]AB[/math] must be parallel to [img]data:image/png;base64,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[/img]. Since we define a parallelogram as a quadrilateral with both pairs of opposite sides parallel, [math]ABCD[/math] is a parallelogram.

Select the statement that must be true.

The height of a parallelogram is greater than the lengths of the sides. Parallelograms have at least one right angle. Parallelograms have congruent diagonals. If a quadrilateral has opposite sides that are both congruent and parallel, then it is a parallelogram.

EFGH is a parallelogram and angle HEF is a right angle.

[img]data:image/png;base64,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[/img][br]Select [b]all [/b]statements that [b]must[/b] be true.

Triangle [math]HEF[/math] is congruent to triangle [math]FGH[/math]. Triangle [math]HEF[/math] is congruent to triangle [math]GFH[/math]. [math]ED[/math] is congruent to [math]HD,DG,[/math] and [math]DF[/math]. Triangle [math]EDH[/math] is congruent to triangle [math]HDG[/math]. [math]EFGH[/math] is a rectangle.

Figure ABCD is a parallelogram.

Is triangle [math]ADB[/math] congruent to triangle [math]CBD[/math]? Show or explain your reasoning.

Figure KLMN is a parallelogram.

Prove that triangle [math]KNL[/math] is congruent to triangle [math]MNL[/math].