**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.

**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