IM Geo.2.8 Lesson: The Perpendicular Bisector Theorem
Which one doesn’t belong?
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J2gT4gkqIR6hTUhHqIR0gjYhnqAS4hHahHSESkgnaBPiCSohHqFNSEeohHSCNiGeoBLiEdqEdIRKSCdoE+IJKiEeoU1IR6iEdII2IZ6gEuIR2oR0hEpIJ2gT4gkqIR6hTUhHqIR0gjYhnqAS4hHahHSESkgnaBPiCSohHqFNSEeohHSCNiGeoBLiEdqEdIRKSCdoE+IJKiEeoU1IR6iEdII2IZ6gEuIR2oR0hEpIJ2gT4gkqIR6hTUhHqIR0gjYhnqAS4hHahHSESkgnaBPiCSohHqFNSEeohHSCNiGeoBLiEdqEdIRKSCdoE+IJKiEeoU1IR6iEdII2IZ6gEuIR2oR0hEpIJ2gT4gkqIR6hTUhHqIR0gjYhnqAS4hHahHSESkgnaBPiCSohHqFNSEeohHSCNiGeoBLiEdqEdIRKSCdoE+IJKiEeoU1IR6iEdII2IZ6gEuIR2oR0hCHh9fV19fPnz96PX79+0V/uWc6/O8tX9Q+9qJDw8+fP1ffv3zs/vn79Wn358uUfSobzUpWQw+rkpEPfjv7+/bv69u3byWu4s2wCSlg2/9l3V8LZERa/gBIWRzBvACWcl1+Gs5UwA4UZMyjhjPCSnKqESUBMHUMJpyaX5zwlzMNi0iRKOCm2VCcpYSoc44dRwvGZZTtDCbMRGTmPEo4MLOFyJUwIZcxISjgmrZxrXyQMmH6YgV8D230N1H8kvEi43+8rP3gZhDQfPnyQHfDr9y8J6x0+shIICeMPTzduAi9NyH0J//bkSsjnr4RwhkoIB1j5j3rxBJUQj9B/1EtHqIR5CD4+PlZPT0+vBornsb9r8+1oVzqAY0pYDtLz8/Ph13oh2vv3719+xXd3d1fFsea+T58+tQ6qhK3RMA4oYTlO9/f3B/EuLy+rh4eHwyDxX428e/euin0hY2z1uuOWrCdXwjoJ6KMSlgN3c3NzkLAWMCa5vb097IvHeovjwantbakS1klBH5WwHLhou/hobtGEFxcXzV2HRgxObVv7kbYz3J8qASUsh+PNmzeH5mtOEFJeXV01dx2eH8vaXKCEzTSAnythGWjx1jKyP36LGfvq7wXryd6+fXv4bynr58ePSnicCOy5EpYBFqJF9s2t/t7v+AcwsS5+ONO2vb5K2yr3p01ACcugie/9jt9ixg9j4i1qc2sTs7lGCZtpAD9XwjLQQsLmT0Bjinge+5tbNOaxrM3j8bkSHicCe66EMGAnxlXCE6GQdikhidbpWZXwdC6YvUqIQdU6qBK2RsM4oIQMTl1TKmFXOoBjSgiA1DOiEvYElP2wEmYn1D+fEvZnlHqFEqbGM2g4JRwUU95FSpiXzdDJlHBoUknXKWFSMCPGUsIRYWVcqoQZqYybSQnH5ZVutRKmQzJ6ICUcHVmuE5QwF48p0yjhlNQSnaOEiWBMHEUJJwaX5TQlzEJi+hxKOD27FGcqYQoMs4ZQwlnxlT9ZCcszmDuBEs5NsPD5SlgYwAK3V8IFQix5CSUsmf4y91bCZXIsdhUlLBb9YjdWwsWiLHMhJSyT+5J3VcIl0yxwLSUsEPrCt1TChQPd+nJKuHXiy99PCZfPdNMrKuGmca9yMyVcJdbtLqqE22W91p2UcK1kN7quEm4U9Iq3UcIVw93i0kq4Rcrr3kMJ18139asr4eoRr34DJVw94nVvoITr5rvF1ZVwi5RXvIcSrhjuRpdWwo2CXus2SrhWsttdVwm3y3qVOynhKrFuelEl3DTu5W+mhMtnuvUVlXDrxBe+nxIuHGiByylhgdCXvKUSLplmmWspYZncF7urEi4WZbELKWGx6Je5sRIuk2PJqyhhyfQXuLcSLhBi4UsoYWEAc2+vhHMTLH++EpZnMGsCJZwVX4qTlTAFhulDKOH07LKcqYRZSEycQwknBpfoNCVMBGPKKEo4JbVc5yhhLh6jp1HC0ZGlO0EJ0yEZN5ASjssr42olzEhlxExKOCKspEuVMCmYoWMp4dCk8q5TwrxsBk2mhINiSr1ICVPj6R9OCfszyr5CCbMT6plPCXsCAhxWQgCkrhGVsCsdxjElZHBqnVIJW6PBHFBCDKrTgyrh6VxIe5WQROvErEp4IhTYLiWEATseVwmPE+E9V0Ies1cTK+GrOJBPlBCJ7c/QSvgnC+pnSkgl9//cSggHWFWVEsIZKiEcoBKeAcDdrtrv9/wX8g+/ApsQDt8mhAO0Cc8AoE2Ih2gTwhHahHCANuEZALQJ8RBtQjhCmxAO0CY8A4A2IR6iTQhHaBPCAdqEZwDQJsRDtAnhCG1COECb8AwA2oR4iDYhHKFNCAdoE54BQJsQD9EmhCO0CeEAbcIzAGgT4iHahHCENiEcoE14BgBtQjxEmxCO0CaEA7QJzwCgTYiHaBPCEdqEcIA2YW6Az8/P1Y8fPzqHVMLOeBAHbcKkmELA6+vr6unpqbq9vW2dUglbo8EcUMKkqD5+/HgQMMZTwqSQFhpLCRcKcsnLPDw8VCFhbI+Pj4ePtuvbhG3JcPYrYUJWV1dX1d3d3WGyrhaMBUqYEODIkZRwZGBrL4/vBUOseIzvB6MVuzYl7EqHcUwJk3G6v7+vLi8vD1P1tWAsUsJkACeMo4QTQlvzlJubmyo+QsBow75NCfsSyn9cCZMxihaM7wnjBzJDNiUcklLuNUqYjE9IGG9Jh25KODSpvOuUMBGbkO/i4mLUREo4Kq6Ui5UwCZb4/i/egh6/Fe1rRSVMAnDGGEo4I7w1To1fS8QPZuLvjMZj3w9nlHANCtteUwm3zXvQ3erfEQ5ZrIRDUsq9Rglz8+mdTgl7I0q/QAnTI+oeUAm78yEcVUICpY4ZlbAjHMghJYSAcszzTUAJz5etrwySgBJCQDnm+SbwH1K8ubPzayHmAAAAAElFTkSuQmCC[/img][/td][/tr][tr][td][img]data:image/png;base64,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[/img][/td][td][img]data:image/png;base64,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[/img][/td][/tr][/table]
Diego, Jada, and Noah were given the following task:
[size=150]Prove that if a point [math]C[/math] is the same distance from [math]A[/math] as it is from [math]B[/math], then [math][/math]C must be on the perpendicular bisector of [math]AB[/math].[br]At first they were really stuck. Noah asked, “How do you prove a point is on a line?” Their teacher gave them the hint, “Another way to think about it is to draw a line that you know [math]C[/math] is on, and prove that line has to be the perpendicular bisector.”[br][br]They each drew a line and thought about their pictures. Here are their rough drafts.[/size][br][br][table][tr][td][br][br]Diego’s approach:[br] “I drew a line through [math]C[/math] that was perpendicular to [math]AB[/math] and [br]through the midpoint of [math]AB[/math]. [br]That line is the perpendicular bisector of [math]AB[/math] and [math]C[/math] is on it,[br] so that proves [math]C[/math] is on the perpendicular bisector.”[/td][td][img]data:image/png;base64,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[/img][/td][/tr][/table][table][tr][td]Jada’s approach:[br] “I thought the line through [math]C[/math] would probably go through [br]the midpoint of [math]AB[/math] so I drew that and labeled the midpoint [math]D[/math]. [br]Triangle [math]ACB[/math] is isosceles, so angles [math]A[/math] and [math]B[/math] are congruent, [br]and [math]AC[/math] and [math]BC[/math] are congruent. And [math]AD[/math] and [math]BD[/math] are congruent [br]because [math]D[/math] is a midpoint. [br]That made two congruent triangles by the Side-Angle-Side [br]Triangle Congruence Theorem. So I know angle [math]ADC[/math] and [br]angle [math]BDC[/math] are congruent, but I still don’t know [br]if [math]DC[/math] is the perpendicular bisector of [math]AB[/math]."[/td][td][img]data:image/png;base64,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[/img][/td][/tr][/table][table][tr][td]Noah’s approach: [br]“In the Isosceles Triangle Theorem proof, [br]Mai and Kiran drew an angle bisector in their isosceles triangle, [br]so I’ll try that. I’ll draw the angle bisector of angle [math]ACB[/math]. [br]The point where the angle bisector hits [math]AB[/math] will be [math]D[/math]. [br]So triangles [math]ACD[/math] and [math]BCD[/math] are congruent, [br]which means [math]AD[/math] and [math]BD[/math] are congruent, [br]so [math]D[/math] is a midpoint and [math]CD[/math] is the perpendicular bisector."[/td][td][img]data:image/png;base64,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[/img][/td][/tr][/table][br][size=150]With your partner, discuss each student’s approach.[/size][list][*]What do you notice that this student understands about the problem?[/*][/list]
[list][*]What question would you ask them to help them move forward?[/*][/list]
Using the ideas you heard and the ways you think each student could make their explanation better, write your own explanation for why [math]C[/math] must be on the perpendicular bisector of [math]A[/math] and [math]B[/math].[br]
[size=150]Elena has another approach: “I drew the line of reflection. If you reflect across C, then A and B will switch places, meaning A' coincides with B, and B' coincides with C. will stay in its place, so the triangles will be congruent.”[/size][br][br]What feedback would you give Elena?
Write your own explanation based on Elena‘s idea.
Work on your own to make a diagram and write a rough draft of a proof for the statement:
If [math]P[/math] is a point on the perpendicular bisector of [math]AB[/math], prove that the distance from [math]P[/math] to [math]A[/math] is the same as the distance from [math]P[/math] to [math]B[/math].
With your partner, discuss each other’s drafts. Record your partner‘s feedback for your proof.
[list][*]What do you notice that your partner understands about the problem?[/*][/list]
[list][*]What question would you ask them to help them move forward?[/*][/list]
IM Geo.2.8 Practice: The Perpendicular Bisector Theorem
Each statement is always true.
Select [b]all[/b] statements for which the converse is also always true.
In isosceles triangle DAC, AD is congruent to AC.
[size=150]Kiran knows that the base angles of an isosceles triangle are congruent. [/size][br]What additional information does Kiran need to know in order to show that [math]AB[/math] is a perpendicular bisector of segment [math]CD[/math]?
Han and Priya were making a kite. Han cut out a piece of fabric so that there were 2 short sides of the same length on top and 2 long sides of the same length on the bottom.
Priya cut 2 pieces of wood to go across the diagonals of the kite. They attached the wood like this:[br][img]data:image/png;base64,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[/img][br][br]Han asked Priya to measure the angle to make sure the pieces of wood were perpendicular. Priya said, “If we were careful about the lengths of the sides of the fabric, we don’t need to measure the angle. It has to be a right angle.”[br]Complete Priya’s explanation to Han.
Prove triangle [math]ADE[/math] is congruent to triangle [math]CBE[/math].
Triangle DAC is isosceles.
What information do you need to show that triangle DBA is congruent to triangle CBA by the Side-Angle-Side Triangle Congruence Theorem?
Write a sequence of rigid motions to take figure [math]CBA[/math] to figure [math]MLK[/math].
Here is a quadrilateral inscribed in a circle.
[size=150]Jada says that it is square because folding it along the horizontal dashed line and then the vertical dashed line gives 4 congruent sides.[/size][br] Do you agree with Jada?