To practice identifying the congruent segments and angles formed by bisectors, let's consider a common shape that includes both segments and angles—a typical "diamond" kite like the ones you can make at home using paper and wooden or plastic sticks.
Study the figure above. Notice that \(\small\mathsf{ \overleftrightarrow{MQ} }\) (line MQ) is a perpendicular bisector of \(\small\mathsf{ \overline{TS} }\).
Which of the following is true?
- \(\small\mathsf{ \overline{SN} }\) and \(\small\mathsf{ \overline{MT} }\)
- \(\small\mathsf{ \overline{NS} }\) and \(\small\mathsf{ \overline{NT} }\)
- \(\small\mathsf{ \overline{MS} }\) and \(\small\mathsf{ \overline{NT} }\)
- \(\small\mathsf{ \overline{SQ} }\) and \(\small\mathsf{ \overline{NT} }\)
Congruent segments are the same size and shape and are created by a perpendicular bisector dividing a segment into two equal halves.
Congruent segments are the same size and shape and are created by a perpendicular bisector dividing a segment into two equal halves.
Congruent segments are the same size and shape and are created by a perpendicular bisector dividing a segment into two equal halves.
Congruent segments are the same size and shape and are created by a perpendicular bisector dividing a segment into two equal halves.
Which angles are congruent right angles?
- ∠SNM and ∠TMN
- ∠QNS and ∠QNT
- ∠QNS and ∠QSN
- ∠SMT and ∠SQT
Congruent angles have the same measure.
Congruent angles have the same measure.
Congruent angles have the same measure.
Congruent angles have the same measure.
Is it possible for segment TS to be the perpendicular bisector?
- yes
- no
Segment TS crosses segment MQ but does not cut it into two equal halves.
Segment TS crosses segment MQ but does not cut it into two equal halves.
Summary
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