Questions and Answers
Which of these shapes is congruent to the given shape?
The pair of triangles that are congruent by the ASA criterion is __________.
triangle ABC and triangle XYZ
The pair of triangles that are congruent by the SAS criterion is __________.
triangle BAC and triangle RQP
If ABC = DEC, what is the value of x?
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If mF = 40°, mA = 80°, and mG = 60°, what is mB?
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Which triangles are congruent according to the SAS criterion?
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What is the next step in the given proof?
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Prove: ∠PCQ is complementary to ∠ABC. What is the missing step in the given proof?
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Which equation is necessarily true when transversal t cuts parallel lines a and b?
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Which statement can be proven true from the diagram showing AB, CD, and GD?
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CD bisects AB at point G. If AE = BE, which equation must be true?
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∠2 ≅ ∠7 The theorem by which they are congruent is the __________.
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Which angles are congruent to ∠2?
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In ΔPQR, PS, QT, and RU are the medians. PS and QT intersect at the point (4, 5). RU intersects PS at what point?
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Given: ΔABC. Prove: A midsegment of ΔABC is parallel to a side of ΔABC. What is the reason for statement 3 in this proof?
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What is m∠ABC when m∠BAC = 70° and ΔABC is an isosceles triangle with AB = AC?
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Given: AC and BD bisect each other. What is the reason for step 3 of this proof?
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In parallelogram LMNO, LM = 4.12, MN = 4, LN = 5, and OM = 6.4. Diagonals LN and OM intersect at point R. What is the length of →?
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Points A(-2, 4), B(1, 3), C(4, -1) and D form a parallelogram. What are the coordinates of D?
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In the figure, AD is __________ centimeters and DC is _________ centimeters.
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Study Notes
Congruence, Proof, and Constructions
- Congruent shapes can be visually identified; the one that looks similar is the likely congruent shape.
- Triangles ABC and XYZ are congruent by the Angle-Side-Angle (ASA) criterion.
- Triangles BAC and RQP are congruent by the Side-Angle-Side (SAS) criterion.
- If triangles ABC and DEC are congruent, then x equals 1.
- Given mF = 40°, mA = 80°, and mG = 60°, angle mB is determined to be 40°.
- Triangles ABC, FGE, and PQR are confirmed congruent under the SAS criterion.
- In a proof, stating CE = DF is justified by the Transitive Property of Equality.
- For proving ∠PCQ complementary to ∠ABC, the missing step involves asserting that corresponding angles are congruent due to parallel lines cut by a transversal.
- If transversal t intersects parallel lines a and b, then the sum of angles m∠3 and m∠5 equals 180°.
- From a given diagram, it can be proven that ∠DGB is supplementary to ∠CGB.
- When CD bisects AB at point G and AE equals BE, then AG must equal BG.
- The congruence of angles ∠2 and ∠7 afirms the use of the Alternate Exterior Angles Theorem.
- Several angles are noted to be congruent to specific angles (e.g., angles congruent to ∠2, ∠6, ∠1, and ∠7).
- Medians PS, QT, and RU of triangle PQR meet at point (4, 5).
- In triangle ABC, a midsegment parallel to a side is justified by the definition of a midpoint.
- In an isosceles triangle where AB equals AC, angle m∠ABC can be calculated based on given conditions.
- The Vertical Angles Theorem supports the reasoning in a proof involving intersecting bisectors AC and BD.
- In parallelogram LMNO, the dimensions given provide a means to find specific lengths, like assessing that the length of certain segments equals 3.2.
- The coordinates of point D can be determined from points A, B, and C, resulting in D being located at (1, 0).
- If lengths are given as 12 cm and 11 cm, segments AD equals 11 cm, while segment DC measures 12 cm.
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Description
Test your knowledge on congruence, proofs, and geometric constructions with this quiz. Review key concepts such as the ASA and SAS criteria for triangle congruence and identify congruent shapes. Perfect for students preparing for geometry tests!
