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e Supply the reason to complete the proof below:| Statements | Reasons | | 1. XQ¯ || TR¯ | 1. Given | | 2. ∠Q ≅ ∠T | 2. Alternate Interior Angles Theorem | | 3. ∠X ≅ ∠R | 3. Alternate Interior Angles Theorem | | 4. XR¯ bisects QT¯ | 4. Given | | 5. TM¯ ≅ QM¯ | 5. Definition of segment bisector | | 6. ΔXMQ ≅ ΔRMT | 6.? |
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e Which postulate can be used to prove that ΔABD ≅ ΔACD if AD¯ bisects ∠BAC and BC¯ ?
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e What additional information is needed to prove that ΔABC ≅ ΔCDA by the AAS Theorem?
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e What postulate is applied to prove that the diagonals of a parellelogram bisect each other?
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| e Do we have enough information to prove that ΔABC ≅ ΔPQR? e |
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| e Is MS¯ ≅ RS¯ ? Given that ∠1 ≅ ∠3, ∠2 ≅∠4, TS ≅ BS e |
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| e What additional information is needed to prove that ΔPQS ≅ ΔTQR by the ASA Postulate? e |
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| e 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? e |
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e 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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| e In the figure, l || m || n. If the two triangles are congruent, then which of the following is correct? e |
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e Supply the reason to complete the proof below:
Given: ∠N ≅ ∠P, MO¯ ≅ QO¯
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e Which of the following can be used to prove that ΔABC ≅ ΔADC?
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| e Which of the following can be applied directly to prove that ΔABC ≅ ΔDEC ? e |
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| e Which of the following can be applied directly to prove that ΔADB ≅ ΔCBD? e |
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| e 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. e |
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e Supply the reason to complete the proof below:| Statements | Reasons | | 1. ∠A @ ∠X and ∠B @ ∠Y | 1. Given | | 2. ∠C @ ∠Z | 2. 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 @ ΔXYZ | 4. ? |
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e Supply the reason to complete the proof below:| Statements | Reasons | | 1. XQ¯ || TR¯ | 1. Given | | 2. ∠Q ≅ ∠T | 2. Alternate Interior Angles Theorem | | 3. ∠X ≅ ∠R | 3. Alternate Interior Angles Theorem | | 4. XR¯ bisects QT¯ | 4. Given | | 5. TM¯ ≅ QM¯ | 5. Definition of segment bisector | | 6. ΔXMQ ≅ ΔRMT | 6.? |
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e Supply the reason to complete the proof where T is the midpoint of PR¯.
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e Supply the reason to complete the proof where T is the midpoint of PR¯.
DDD |
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DDD | Statements | Reasons | | 1. ÐAEB @ ÐBDC | 1.Given | | 2. AE¯ @ BD¯ | 2.Given | | 3. AE¯|| BD¯ | 3.Given | | 4. ÐEAB @ ÐDBC | 4. Corresponding Angles Theorem | | 5. ΔAEB @ ΔBDC | 5.? |
Supply the reason to complete the proof below:
Given: AE¯|| BD¯, AE¯ ≅ BD¯, ∠E ≅ ∠D. DDD |
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DDD Supply the reason to complete the proof below:
Given: ∠N ≅ ∠P, MO¯ ≅ QO¯
DDD |
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