Question

The different pairs of equivalent angles resemble some letters of the alphabet. Classify the angle pairs based on the letter of alphabet that they make. Refer the three diagrams below.

Accepted Answer

In the above figure, the angles $∠ N M B$ and $∠ E M A$ resembles the alphabet $X$ .

Here, $∠ N M B = ∠ E M A$

$∠ N M B$ and $∠ E M A$ are formed due to intersection of the line segments $A B$ and $E N$ .

We know that when two lines intersect each other, then the opposite angles, formed due to intersection are called vertically opposite angles.

Therefore, $∠ N M B$ and $∠ E M A$ are vertically opposite angles.

In the above figure, the angles $∠ P N H$ and $∠ K M N$ resembles the alphabet $F$ .

Here, $∠ P N H = ∠ K M N$

$∠ P N H$ and $∠ K M N$ are formed when a transversal line $M H$ cut two parallel lines $M K$ and $N P$ .

We know that angles formed when a transversal line cut two parallel lines are known as corresponding angles.

Therefore, $∠ P N H$ and $∠ K M N$ are corresponding angles.

In the above figure, the line segments that make the angles $∠ X M N$ and $∠ M N Q$ resembles the alphabet $Z$ .

Here, $∠ X M N = ∠ M N Q$

$∠ X M N$ and $∠ M N Q$ are formed when a transversal line $S M$ cut two parallel lines $M X$ and $N Q$ .

We know that when two straight lines are cut by a transversal, then the angles formed on the opposite side of the transversal with respect to both the lines are called alternate angles.

Therefore, $∠ X M N$ and $∠ M N Q$ are alternate angles.

David Weber, Talei Kunkel, Harriet Simand and, Justin Medved Solutions for Chapter: Geometric Constructions Artistry and Creativity, Exercise 18: Reflect and discuss 7

David Weber Mathematics Solutions for Exercise - David Weber, Talei Kunkel, Harriet Simand and, Justin Medved Solutions for Chapter: Geometric Constructions Artistry and Creativity, Exercise 18: Reflect and discuss 7

Questions from David Weber, Talei Kunkel, Harriet Simand and, Justin Medved Solutions for Chapter: Geometric Constructions Artistry and Creativity, Exercise 18: Reflect and discuss 7 with Hints & Solutions

Learn and Prepare for any exam you want !