P Preliminary Concepts 1 Line And Angle Relationships 2 Parallel Lines 3 Triangles 4 Quadrilaterals 5 Similar Triangles 6 Circles 7 Locus And Concurrence 8 Areas Of Polygons And Circles 9 Surfaces And Solids 10 Analytic Geometry 11 Introduction To Trigonometry A Appendix Chapter5: Similar Triangles
5.1 Ratios, Rates And Proportions 5.2 Similar Polygons 5.3 Proving Triangles Similar 5.4 The Pythagorean Theorem 5.5 Special Right Triangles 5.6 Segments Divided Proportionally 5.CR Review Exercises 5.CT Test Section5.4: The Pythagorean Theorem
Problem 1E: By naming the vertices in order, state three different triangles that are similar to each other.... Problem 2E: Use theorem 5.4.2 to form a proportion in which SV is a geometric mean. Hint: SVTRVS Exercises 1-6 Problem 3E: Use theorem 5.4.3 to form a proportion in which RS is a geometric mean. Hint RVSRST Exercises 1-6 Problem 4E: Use theorem 5.4.3 to form a proportion in which TS is a geometric mean. Hint: TVSTSR Exercises 1-6 Problem 5E: Use theorem 5.4.2 to find RV if SV=6 and VT=8. Exercises 1-6 Problem 6E Problem 7E: Find the length of DF if: a DE=8 and EF=6. b DE=5 and EF=3. Exercises 7-10 Problem 8E: Find the length of DE if: a DF=13 and EF=5. b DE=12 and EF=63. Exercises 7-10 Problem 9E: Find EF if: a DF=17 and DE=15. b DF=12 and DE=82. Exercises 7-10 Problem 10E: Find DF if: a DE=12 and EF=5 b DF=12 and EF=6. Exercises 7-10 Problem 11E: Determine whether each triple (a,b,c) is a Pythagorean triple.... Problem 12E Problem 13E Problem 14E: Determine the type of triangle represented if the lengths of its sides are: a a=1.5, b= 2 and c =... Problem 15E: A guy wire 25 ft long supports an antenna at a point that is 20 ft above the base of the antenna.... Problem 16E: A strong wind holds a kite 30 ft above the earth in a position 40 ft across the ground. How much... Problem 17E: A boat is 6 m below the level of a pier and 12 m from the pier as measured across the water. How... Problem 18E: A hot-air balloon is held in place by the ground crew at a point that is 21 ft from a point directly... Problem 19E: A drawbridge that is 104 ft in length is raised at its midpoint so that the uppermost points are 8... Problem 20E: A drawbridge that is 136 ft in length is raised at its midpoint so that the uppermost points are 16... Problem 21E: A rectangle has a width of 16 cm and a diagonal of length 20 cm. How long is the rectangle? Problem 22E: A right triangle has legs of lengths x and 2x2 and a hypotenuse of length 2x3. What are the lengths... Problem 23E: A rectangle has base length x3, altitude length x1, and diagonals of length 2x each. What are the... Problem 24E: The diagonals of a rhombus measure 6 m and 8 m. How long are each of the congruent sides? Problem 25E: Each side of a rhombus measure 12 in. If one diagonal is 18 in. long, how long is the other... Problem 26E: An isosceles right triangle has a hypotenuse of length 10 cm. How long is each leg? Problem 27E Problem 28E: In right ABC with right C, AB=10 and BC=8. Find the length of MB if M is the midpoint of AC. Problem 29E Problem 30E Problem 31E: Find the length of the altitude to the 26-in. side of a triangle whose sides are 10, 24, and 26 in.... Problem 32E Problem 33E: In quadrilateral RSTU, RSST and UT diagonal RT. If RS=6, ST= 8, and RU = 15, determine UT. Problem 34E Problem 35E: If a=p2q2,b=2pq and c=p2+q2, show that c2=a2+b2. Problem 36E Problem 37E Problem 38E: When the rectangle in the accompanying drawing whose dimensions are 16 by 9 is cut into pieces and... Problem 39E: A, C and F are three of the vertices of the cube shown in the accompanying figure. Given that each... Problem 40E Problem 41E: In the figure, square RSTV has its vertices on the sides of square WXYZ as shown. If ZT=5 and TY=12... Problem 42E: Prove that if (a,b,c) is a Pythagorean triple and n is a natural number, the (na,nb,nc) is also a... Problem 43E: Use Figure 5.19 to prove Theorem 5.4.2. Theorem 5.4.2 The length of the altitude to the hypotenuse... Problem 44E: Use Figures 5.20 and 5.21 to prove Lemma 5.4.3. Lemma 5.4.3 The length of each leg of a right... Problem 45E Problem 35E: If a=p2q2,b=2pq and c=p2+q2, show that c2=a2+b2.
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Linear Algebra
True or false
Transcribed Image Text: If BC = BD
then C= D
5.
5 If AB = BA and A
is in lertible
then A? B =BA-
Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.
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