Core Connections Integrated II, 2015
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Core Connections Integrated II, 2015 View details
3. Section 1.3
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Exercise 87 Page 48

Practice makes perfect
a When we fold something over itself, each angle on one half of the shape will pair up with a corresponding angle on the other half. However, for a kite the line of symmetry runs through two of the kite's vertices, which means we only have one pair of angles with equal measures in the original shape that pair up.
b As in Part A, we have to draw the line of symmetry through one of the triangle's vertices. Therefore, we only have one pair of angles with equal measures in the original shape.


c For an equilateral triangle we have 3 lines of symmetry, each of them passing through one of the vertices and the midpoint of the opposite side.

Depending on how you fold the triangle, an angle can be mapped onto all other angles. This means they must all have the same measure.

d A rhombus has two lines of symmetry.

With this, we see that a rhombus has two pairs of angles with equal measures.