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ABCD is a quadrilateral with AB equal and parallel to DC. Prove that AD is equal and parallel to BC. nted by the

ABCD is a quadrilateral with AB equal and parallel to DC. Prove that AD is equal and parallel to BC. nted by the

Elementary Geometry for College Students
Elementary Geometry for College Students
6th Edition
ISBN:9781285195698
Author:Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:Daniel C. Alexander, Geralyn M. Koeberlein
Chapter3: Triangles
Section3.CT: Test
Problem 8CT: CM is the median for ABC from vertex C to side AB. a Name two line segments that must be congruent....
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AB+ AD +CB+CD%D 6. ABCD is a quadrilateral with AB equal and parallel to DC. Prove that AD is equal and parallel to BC. OABC is a square and the line segments OA, OB, OC are represented by the vectors a, b, e respectively. If D is the midpoint of BC, show that the line segment a or (b+ c). Verify that each of 21 OD is represented by either e + a or b 2. ation
Transcribed Image Text:AB+ AD +CB+CD%D 6. ABCD is a quadrilateral with AB equal and parallel to DC. Prove that AD is equal and parallel to BC. OABC is a square and the line segments OA, OB, OC are represented by the vectors a, b, e respectively. If D is the midpoint of BC, show that the line segment a or (b+ c). Verify that each of 21 OD is represented by either e + a or b 2. ation
and y. What can you deduce about the directed line-segments BC and PQ7 4. ABC is a triangle. If D is the midpoint of AC, show that BA + BC 2BD. [BD is known as the median of the triangle ABC.] ABCD is a quadrilateral and P and Q are the midpoints of AC and BD respectively. Show that AB+ AD+CB+ CD 4 PQ. 6. ABCD is a quadrilateral with AB equal and parallel to DC. Prove that AD is equal and parallel to BC. OABC is a square and the line segments OA, OB, OC are represented by the vectors a, b, c respectively. If D is the midpoint of BC, show that the line segment OD is represented by either e+ a or b- (b + c). Verify that each of a or these can be obtained from either of the others by using the relation b=a+c. ABCD is a square and P, Q are the midpoints of BC, CD respectively. If AP a and AQ b, find in terms of a and b, the directed line segments (i) AB, (ii) AD, iii) BD, (iv) AC. In a quadrilateral OABC, D is the midpoint of BC and E is the point on AD such mat AE:ED 2: 1. Given that OA=a, OB-b, OC e, express OD and OE in ms of a, b, c. ABC is a tetrahedron and OA a, OB-b and OC c. The points P and Q are h that OA AP and 20B- BQ. The point M is the midpoint of PQ. Find %3D () AB, (i) PQ. (ii) CQ, (iv) QM, (v) MB, (vi) OM Erms of a, b and c. [For the definition of a tetrahedron, see Sec 1.10 Fir
Transcribed Image Text:and y. What can you deduce about the directed line-segments BC and PQ7 4. ABC is a triangle. If D is the midpoint of AC, show that BA + BC 2BD. [BD is known as the median of the triangle ABC.] ABCD is a quadrilateral and P and Q are the midpoints of AC and BD respectively. Show that AB+ AD+CB+ CD 4 PQ. 6. ABCD is a quadrilateral with AB equal and parallel to DC. Prove that AD is equal and parallel to BC. OABC is a square and the line segments OA, OB, OC are represented by the vectors a, b, c respectively. If D is the midpoint of BC, show that the line segment OD is represented by either e+ a or b- (b + c). Verify that each of a or these can be obtained from either of the others by using the relation b=a+c. ABCD is a square and P, Q are the midpoints of BC, CD respectively. If AP a and AQ b, find in terms of a and b, the directed line segments (i) AB, (ii) AD, iii) BD, (iv) AC. In a quadrilateral OABC, D is the midpoint of BC and E is the point on AD such mat AE:ED 2: 1. Given that OA=a, OB-b, OC e, express OD and OE in ms of a, b, c. ABC is a tetrahedron and OA a, OB-b and OC c. The points P and Q are h that OA AP and 20B- BQ. The point M is the midpoint of PQ. Find %3D () AB, (i) PQ. (ii) CQ, (iv) QM, (v) MB, (vi) OM Erms of a, b and c. [For the definition of a tetrahedron, see Sec 1.10 Fir
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