Intersecting | Class 7 Mathematics Notes

5.8 Alternate Angles

This section explains alternate angles formed when a transversal intersects two parallel lines. Alternate angles are pairs of angles that lie on opposite sides of the transversal but inside the two lines. For example, in the figure, angle d is the alternate angle of angle f, and angle c is the alternate angle of angle e. The section shows how to find an alternate angle by first identifying the corresponding angle and then the vertically opposite angle to it. Using the properties of corresponding and vertically opposite angles, it is proved that alternate angles are equal when the lines are parallel. An activity asks students to find the measure of an alternate angle given the measure of its corresponding angle. The section also introduces interior angles on the same side of the transversal, which always add up to 180°. Several examples demonstrate calculating unknown angles using these properties, reinforcing the understanding of angle relationships in parallel lines intersected by a transversal.

📊 Diagram: Fig. 5.25 shows alternate angles d and f, and c and e formed by transversal intersecting parallel lines; Figs. 5.26 to 5.29 show examples calculating angles using alternate and corresponding angles.

🧪 Activity: Activity 6: Given angle f, find the measure of its alternate angle d using properties of corresponding and vertically opposite angles.

🔗 Connection: This section's understanding of alternate angles and interior angles prepares students for solving complex angle problems and recognizing parallelism in figures.