ssrs barcode font free 15.4B Sketching Triangles to be Constructed in Objective-C

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15.4B Sketching Triangles to be Constructed
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Before doing the actual construction, it is very helpful to make a preliminary sketch of the required triangle. In this sketch: 1. 2. 3. 4. Show the position of each of the given parts of the triangle. Draw the given parts heavy, the remaining parts light. Approximate the sizes of the given parts. Use small letters for sides to agree with the capital letters for the angles opposite them.
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Fig. 15-11
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As an example, you might make a sketch like that in Fig. 15-11 before constructing a triangle given two angles and an included side.
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CHAPTER 15 Constructions
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15.4C Triangle Constructions
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CONSTRUCTION
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To construct a triangle given its three sides
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Given: Sides of lengths a, b, and c (Fig. 15-12) To construct: ^ABC Construction: On a working line w, construct AC such that AC b. With A as center and c as radius, construct arc (1). Then with C as center and a as radius, construct arc (2) intersecting arc (1) at B. Draw BC and AB. ^ABC is the required triangle.
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Fig. 15-12
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CONSTRUCTION
Fig. 15-13
To construct an angle of measure 60
Given: Line w (Fig. 15-13) To construct: An angle of measure 60 Construction: Using a convenient length as a side, construct an equilateral triangle using construction 7. Then any angle of the equilateral triangle is the required angle.
CONSTRUCTION
To construct a triangle given two sides and the included angle
Given: jA, segments of lengths b and c (Fig. 15-14) To construct: ^ABC Construction: On a working line w, construct AC such that AC b. At A, construct jA with one side AC. On the other side of jA, construct AB such that AB c. Draw BC. Then the required triangle is ^ABC.
Fig. 15-14
CONSTRUCTION
10: To construct a triangle given two angles and the included side
Given: jA, jC, and a segment of length b (Fig. 15-15) To construct: ^ABC Construction: On a working line w, construct AC such that AC b. At A, construct jA with one side on AC, and at C, construct jC with one side on AC. Extend the new sides of the angles until they meet at B.
Fig. 15-15
CHAPTER 15 Constructions
11: To construct a triangle given two angles and a side not included
CONSTRUCTION
Given: jA, jB, and a segment of length b (Fig. 15-16) To construct: ^ABC Construction: On a working line w, construct AC such that AC b. At C, construct an angle with measure equal to mjA mjB so that the extension of AC will be one side of the angle. The remainder of the straight angle at C will be jC. At A, construct jA with one side on AC. The intersection of the new sides of the angles is B.
Fig. 15-16
Fig. 15-17
CONSTRUCTION
12: To construct a right triangle given its hypotenuse and a leg
Given: Hypotenuse with length c and leg with length b of right triangle ABC (Fig. 15-17) To construct: Right triangle ABC Construction: On a working line w, construct AC such that AC b. At C construct a perpendicular to AC. With A as center and a radius of c, construct an arc intersecting the perpendicular at B.
SOLVED PROBLEMS
15.5 Constructing a triangle Construct an isosceles triangle, given the lengths of the base and an arm (Fig. 15-18).
Fig. 15-18
Solution
Use construction 7, since all three sides of the triangle are known.
15.6 Constructing angles based on the construction of the 60 angle Construct an angle of measure (a) 120 ; (b) 30 ; (c) 150 ; (d ) 105 ; (e) 75 .
Solutions
(a) Use construction 8 [Fig. 15-19(a)] to construct 120 as 180 60 . (b) Use constructions 8 and 3 to construct 30 as 1(60 ) [Fig. 15-19(b)]. 2 (c) Use (b) to construct 150 as 180 30 [Fig. 15-19(b)].
CHAPTER 15 Constructions
(d) Use constructions 3, 4, and 8 to construct 105 as 60 (e) Use (d) to construct 75 as 180 105 [Fig. 15-19(c)].
1 2 (90
) [Fig. 15-19(c)].
Fig. 15-19
15.5 Constructing Parallel Lines
CONSTRUCTION
13: To construct a line parallel to a given line through a given external point
Given: AB and external point P (Fig. 15-20) 4 To construct: A line through P parallel to AB 4 4 4 Construction: Draw a line RS through P intersecting AB in Q. Construct jSPD jPQB. Then CD is the required parallel. (If two corresponding angles are congruent, the lines cut by the transversal are parallel.)
Fig. 15-20
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