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Solved Examples
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ff  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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ff  Supply the reason to complete the proof where T is the midpoint of PR¯.
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ff  Supply the reason to complete the proof below:
Given: N P, MO¯ QO¯
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ff  Which of the following is true?
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ff  Which postulate can be used to prove that ΔABD ΔACD if AD¯ bisects BAC and BC¯ ?
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ff  What additional information is needed to prove that ΔABC ΔCDA by the AAS Theorem?
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ff  What postulate is applied to prove that the diagonals of a parellelogram bisect each other?
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ff  Do we have enough information to prove that ΔABC ΔPQR?  ff View Solution
ff  Is MS¯ RS¯ ? Given that 1 3, 2 4, TS BS  ff View Solution
ff  What additional information is needed to prove that ΔPQS  ΔTQR by the ASA Postulate?  ff View Solution
ff  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?  ff View Solution
ff  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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ff  In the figure, l || m || n. If the two triangles are congruent, then which of the following is correct?  ff View Solution
ff  Supply the reason to complete the proof below:
Given: N P, MO¯ QO¯
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ff  Which of the following is true?
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ff  Is ΔABC ΔPQR?
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ff  Is ΔABC ΔPQR?  ff View Solution
ff  Which of the following can be used to prove that ΔABC ΔADC?
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ff  Is ΔABD ΔACD?  ff View Solution
ff  Which of the following can be applied directly to prove that ΔABC ΔDEC ?  ff View Solution
ff  Which of the following can be applied directly to prove that ΔADB ΔCBD?  ff View Solution
ff  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.  ff View Solution
ff  Is ΔABC ΔEDC?
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ff  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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ff  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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ff  Is ΔABC ΔPQR?  ff View Solution
ff  Supply the reason to complete the proof where T is the midpoint of PR¯.
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ff  
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.  ff
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ff  Are the triangles congruent?
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