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**Geometry Mini-Lesson AB = 4, DE = 4, m BAC = m EDF**

These two triangles were on Yin's geometry exam. Which of the following statements will prove that triangle ABC is congruent to triangle DEF? AB = 4, DE = 4, m BAC = m EDF BC = 6, EF = 6, m BAC = m EDF AB = 4, DE = 4, m ABC = m DEF BC = 6, EF = 6, m ABC = m DEF MA.912.G.8.4: Make conjectures with justifications about geometric ideas. Distinguish between information that supports a conjecture and the proof of a conjecture.

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Geometry Mini-Lesson Given that m BCD = 50°, which of the following statements is sufficient to prove that ΔBCD is an isosceles triangle? m ABD = 100° m BDC + m CBD + 50° = 180° m BDC + 50° = m ABD m ABD + m CBD = 180° MA.912.G.8.4: Make conjectures with justifications about geometric ideas. Distinguish between information that supports a conjecture and the proof of a conjecture.

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Geometry Mini-Lesson Given that m BAC = 20°, which of the following statements will prove Δ ABC is isosceles? m ABC + m BCA + 20° = 180° m ABC + 20° = m BCD m BCD = 40° m ACB + m BCD = 180° MA.912.G.8.4: Make conjectures with justifications about geometric ideas. Distinguish between information that supports a conjecture and the proof of a conjecture.

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**Geometry Mini-Lesson AE = DE AB = CD m EAB = m EDC m EBA = m ECD**

Use the figure below to determine which of the following conditions is sufficient to prove that ΔBEC is isosceles? AE = DE AB = CD m EAB = m EDC m EBA = m ECD MA.912.G.8.4: Make conjectures with justifications about geometric ideas. Distinguish between information that supports a conjecture and the proof of a conjecture.

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**Geometry Mini-Lesson m ADC = 90° m BAD = 90° m BCD = 90° m ACB = 60°**

On Jamal's geometry test, quadrilateral ABCD is inscribed in a circle. Use the figure to determine which of the following statements is sufficient to prove that ΔABC is a right triangle? m ADC = 90° m BAD = 90° m BCD = 90° m ACB = 60° MA.912.G.8.4: Make conjectures with justifications about geometric ideas. Distinguish between information that supports a conjecture and the proof of a conjecture.

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Geometry Mini-Lesson Tomas saw the following figure of parallelogram ABCD in his geometry book. Which of the following statements will prove that parallelogram ABCD is a rectangle? m ABC + m BCD = 180° m ABC + m CDA = 180° m BCD + m CDA = 180° m CDA + m DAB = 180° MA.912.G.8.4: Make conjectures with justifications about geometric ideas. Distinguish between information that supports a conjecture and the proof of a conjecture.

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Geometry Mini-Lesson Janet makes the conjecture that line p is also parallel to line r. What must the value of y be for her conjecture to be correct? MA.912.G.8.4: Make conjectures with justifications about geometric ideas. Distinguish between information that supports a conjecture and the proof of a conjecture.

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**Geometry Mini-Lesson AB = 7, CD = 7, m ABC = m ADC**

The following figure was on a quiz in Jaime's geometry class. Which of the following statements will prove that ΔABC is congruent to ΔCDA? AB = 7, CD = 7, m ABC = m ADC AD = 10, BC = 10, m ACD = m BAC AB = 7, CD = 7, m CAD = m ACB AD = 10, BC = 10, m ACB = m CAD MA.912.G.8.4: Make conjectures with justifications about geometric ideas. Distinguish between information that supports a conjecture and the proof of a conjecture.

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Geometry Mini-Lesson Maria inscribed ΔABC in a circle. Which of the following statements will prove that ΔABC is a right triangle? BAC is acute. ACB is obtuse. AB = 3, AC = 5 Arc ABC is a semicircle. MA.912.G.8.4: Make conjectures with justifications about geometric ideas. Distinguish between information that supports a conjecture and the proof of a conjecture.

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