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Solved Examples
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fff Supply the reason to complete the proof below:
StatementsReasons
1. XQ¯ || TR¯1. Given
2. Q T2. Alternate Interior Angles Theorem
3. X R3. Alternate Interior Angles Theorem
4. XR¯ bisects QT¯4. Given
5. TM¯ QM¯5. Definition of segment bisector
6. ΔXMQ ΔRMT6.?
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fff Supply the reason to complete the proof where T is the midpoint of PR¯.
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fff Supply the reason to complete the proof below:
Given: N P, MO¯ QO¯
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fff Which of the following is true?
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fff Which postulate can be used to prove that ΔABD ΔACD if AD¯ bisects BAC and BC¯ ?
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fff What additional information is needed to prove that ΔABC ΔCDA by the AAS Theorem?
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fff What postulate is applied to prove that the diagonals of a parellelogram bisect each other?
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fff Do we have enough information to prove that ΔABC ΔPQR? fff View Solution
fff Is MS¯ RS¯ ? Given that 1 3, 2 4, TS BS fff View Solution
fff What additional information is needed to prove that ΔPQS  ΔTQR by the ASA Postulate? fff View Solution
fff Isosceles triangles ABC and PQR are congruent. Angle bisectors of ABC and ACB meet at D. Angle bisectors of PQR and PRQ meet at M. With what postulate of congruency of triangles can you prove that BD = QM? fff View Solution
fff To prove that ΔADC ΔAEC, what additional data is required?
I. ADC = ACE
II. ACD = ACE
III. AC bisects DAE
IV. AD BC
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fff In the figure, l || m || n. If the two triangles are congruent, then which of the following is correct? fff View Solution
fff Supply the reason to complete the proof below:
Given: N P, MO¯ QO¯
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fff Which of the following is true?
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fff Is ΔABC ΔPQR?
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fff Is ΔABC ΔPQR? fff View Solution
fff Which of the following can be used to prove that ΔABC ΔADC?
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fff Is ΔABD ΔACD? fff View Solution
fff Which of the following can be applied directly to prove that ΔABC ΔDEC ? fff View Solution
fff Which of the following can be applied directly to prove that ΔADB ΔCBD? fff View Solution
fff ABCD is a square, and F is the midpoint of line segment EB. Find the number of triangles that are congruent to ΔOAD with respect to ASA Theorem. fff View Solution
fff Is ΔABC ΔEDC?
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fff Supply the reason to complete the proof below:
StatementsReasons
1. A @ X and B @ Y1. Given
2. C @ Z2. If two angles of one triangle are congruent to two angles of another triangle then the third angles are congruent.
3. BC¯ @ YZ¯3. Given
4. ΔABC @ ΔXYZ4. ?

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fff Supply the reason to complete the proof below:
StatementsReasons
1. XQ¯ || TR¯1. Given
2. Q T2. Alternate Interior Angles Theorem
3. X R3. Alternate Interior Angles Theorem
4. XR¯ bisects QT¯4. Given
5. TM¯ QM¯5. Definition of segment bisector
6. ΔXMQ ΔRMT6.?
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fff Is ΔABC ΔPQR? fff View Solution
fff Supply the reason to complete the proof where T is the midpoint of PR¯.
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fff 
StatementsReasons
1. ÐAEB @ ÐBDC1.Given
2. AE¯ @ BD¯2.Given
3. AE¯|| BD¯3.Given
4. ÐEAB @ ÐDBC4. Corresponding Angles Theorem
5. ΔAEB @ ΔBDC5.?
Supply the reason to complete the proof below:
Given: AE¯|| BD¯, AE¯ BD¯, E D. fff
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fff Are the triangles congruent?
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