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Authors:Zvezdelina Stankova, Zdravka Paskaleva, Maya Alashka, Raina Alashka

Pages: 132

ISBN: 978-954-779-238-8

Available: Paperback & PDF

In the 7B books, students will see great growth in mathematical maturity.

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Overview

Students will work through a classical axiomatic approach to geometry, beginning with basic axioms and definitions, moving on to a thorough examination of parallel lines, triangle congruence theorems, and the basics of Euclidean constructions. Emphasis is placed on clear, logical thinking and writing. In algebra, students learn to solve linear equations, as well as equations that reduce to linear ones: reducible quadratics, the absolute value of linear and factored quadratics.

The modeling and applications are more advanced, and students learn methods for clearly organizing their thoughts and work as they solve word problems on motion, work, mixtures and alloys, along with basic finance. The year closes with review, giving students a reminder just how much they have grown.

Chapter 7. Foundations of Geometry
80. Ray, Half-plane, and Angle……………………………..206
81. Supplementary Angles. Right Angles…………………..206
82. Vertical Angles. Perpendicular Lines……………………… 207
83. Criterion for Parallel Lines ……………………………..207
84. Criteria for Parallel Lines. Exercises………………..208
85. Axiom of Parallel Lines………………………………….209
86. Properties of Parallel Lines……………………………..209
87. Triangle ………………………………………………………..209
88. Sum of the Angles in a Triangle……………………….210
89. Exterior Angle of a Triangle ……………………………210
90. Triangle. Exercises…………………………………………211
91. Summary of “Foundations of Geometry” ………….213

Chapter 8. Part I: Linear Equations
94. Equation with One Unknown…………………………..214
95. Equivalent Equations……………………………………..214
96. The Equation ax + b = 0, I ………………………………215
97. The Equation ax + b = 0, II……………………………..216
98. The Equation (ax + b)(cx + d) = 0…………………….218
99. The Equation |ax + b| = c ………………………………..219
100. Equations that Reduce to Linear Ones………………220
101. Linear Parametric Equations……………………………222
102. Summary of “Linear Equations”………………………223
Chapter 8. Part II: Modeling and Applications
104. Modeling with Linear Equations, I ……………………224
105. Modeling with Linear Equations, II…………………..225
106. Word Problems on Motion, I……………………………226
107. Word Problems on Motion, II ………………………….227
108. Word Problems on Work, I………………………………228
109. Word Problems on Work, II …………………………….229
110. Word Problems on Interest Rates and Capital ………..230
111. Word Problems on Mixtures and Alloys……………231
112. Summary of “Modeling and Applications”………..233

Chapter 9. Part I: Criteria for Congruence of D’s
114. Congruent Triangles. Introduction ……………………234
115. SAS Criterion for Congruence of Triangles……….234
116. SAS Criterion for Congruence of D’s. Exercises…235
117. ASA Criterion for Congruence of Triangles ………236
118. SAS/ASA Criteria for Congruence of D’s. Exercises..238
119. Isosceles Triangle…………………………………………..239
120. Isosceles & Equilateral Triangle. Exercises…………240
121. Perpendicular Bisector of a Segment………………..241
122. Perpendicular Bisector of a Segment. Exercises…242
123. SSS Criterion for Congruence of Triangles……….244
124. Perpendicular from a Point to a Line ………………..245
125. Right Triangle with Angle 30° …………………………245
126. Right Triangle with Angle 30°. Exercises………….246
127. Median to the Hypotenuse of a Right Triangle…..248
128. Median to the Hypotenuse. Exercises……………….248
129. SSR Criterion for Congruence of Right Triangles… 250
130. Angle Bisector……………………………………………….251
131. Angle Bisector. Exercises………………………………..252
132. Isosceles D: Altitude, Angle Bisector, and Median … 253
133. Equivalent Statements…………………………………….255
134. Summary of “Congruent Triangles” …………………256
Chapter 9. Part II: Euclidean Constructions
137. Constructions w/ a Ruler and a Compass, I……….257
138. Constructions w/ a Ruler and a Compass, II………259
139. Constructing a Triangle by SAS ………………………260
140. Constructing a Triangle by ASA………………………261
141. Summary of “Construction Problems” ……………..262

Chapter 10. Yearly Review149. Test with Solutions on 7A Material……………………263
156. Yearly Review Test with Solutions…………………..265

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