Given: YZ and WZ are tangent to drde X, mWY =90°. Prove: WXYZ Is a square. Y. W Z because it is a central angle. Because a line tangent to a circle is Because mWY =90°, m YXW = a line perpendicular to a radius at the point of tangency, XYZ and ZXWZ are right angles. The sum of the measures of the angles of a quadrilateral is 360°, so mzWZY = %3D . Thus all 4 angles of WXYZ are right, so WXYZ is a (select) one pair of consecutive congruent sides is a (select) is both a rectangle and a rhombus, it (select) v.XY (select) v because they are radii. Because a parallelogram with v,WXYZ is a (select) v.Since WXYZ v also be a square.

Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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Given: YZ and WZ are tangent to drde X, mWY=90°.
Prove: WXYZ Is a square.
Y
W
because it is a central angle. Because a line tangent to a circle is
Because mWY= 90°, mYXW =
a line perpendicular to a radius at the point of tangency, XYZ and ZXWZ are right angles. The sum of
the measures of the angles of a quadrilateral is 360°, so mzWZY =
P.Thus all 4 angles of WXYZ are
right, so WXYZ is a (select)
one pair of consecutive congruent sides is a (select)
is both a rectangle and a rhombus, it (select)
v.XY (select) Y because they are radii. Because a parallelogram with
WXYZ is a (select)
v. Since WXYZ
v also be a square.
Transcribed Image Text:Given: YZ and WZ are tangent to drde X, mWY=90°. Prove: WXYZ Is a square. Y W because it is a central angle. Because a line tangent to a circle is Because mWY= 90°, mYXW = a line perpendicular to a radius at the point of tangency, XYZ and ZXWZ are right angles. The sum of the measures of the angles of a quadrilateral is 360°, so mzWZY = P.Thus all 4 angles of WXYZ are right, so WXYZ is a (select) one pair of consecutive congruent sides is a (select) is both a rectangle and a rhombus, it (select) v.XY (select) Y because they are radii. Because a parallelogram with WXYZ is a (select) v. Since WXYZ v also be a square.
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