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A Side with an Expression

Part of the Triangles section of Coddy's Geometry journey. Lesson 49 of 60.

When a side is written with a letter, the proportion becomes an equation. Pair the sides by the matching corners, write the two ratios equal, and solve.

$Similar triangles ABC and DEF, with DE equal to x plus 2$

The arcs give ∠A = ∠D and ∠B = ∠E, so △ABC ~ △DEF. AB matches DE and CA matches FD: $\frac{4}{x+2} = \frac{3}{6}$ . The right side is 1/2, so x + 2 = 8 and $x = 6$ . Check: DE = 8 is twice AB, like FD is twice CA.

On the board, tap the four sides, pick Similar triangles, and the board writes the proportion. Then clear the fractions with the moves.

Challenge

The arcs show △ABC ~ △DEF. Tap the sides you need, pick the rule, and solve the equation the board writes for x.

Then press Check.

Try it yourself

$Use the figure to find x$

Use the figure to find x

All lessons in Triangles

1The Triangle Inequality

Can Three Sticks Meet?Exactly Reaching The Range of the Third Side Recap: The Third Side

4Area of a Triangle

Half the Rectangle Height Is Not a Side Right Triangle Area Finding the Height Any Side Can Be the Base Recap: Area

7Is It Right?

The Converse Testing a Triangle Acute or Obtuse?Sorting by the Test Recap: Right or Not

10Scale in the World

Shadows Across the River Nested TrianglesA Side with an ExpressionRecap: Scale in the World

2Sides and Names

Sorting by Sides The Longest Side Ticks into Equations Recap: Sorting Triangles

5The Pythagorean Theorem

Squares on the Sides Finding the Hypotenuse Pythagorean Triples When It Is Not Whole Recap: The Hypotenuse

8Special Right Triangles

The 45-45-90 Triangle Legs from the Hypotenuse The 30-60-90 Triangle All Three Sides Which Triangle Is It?Recap: Special Triangles

11Two Tools at Once

Height of an Isosceles Area from the Height The Equilateral Triangle Right Triangle Perimeter Recap: Two Tools