CONSECUTIVE TRIANGLES

CONSECUTIVE TRIANGLES – GEOMETRY QUESTION

Fridays we’re presenting more challenging math practice, most of them being Algebra and Geometry. When a formula is needed, it will be provided. This week we are presenting Consecutive Triangles, a Geometry question. You will need to use the Pythagorean formula.

In a right triangle, the sum of the squares of the two legs is equal to the square of the hypotenuse.

a² + b² = c²            

QUESTION:

If OA = 5, what is the measure of OG?

ANSWER: OG = 5√7

◺ABC is an isosceles right triangle, so the hypotenuse, OB = 5√2.

Now, ◺CBO, has legs of 5 and 5√2. Use the Pythagorean theorem.

CO = 5² + (5√2)² = √75 = 5√3

In ◺DCO, leg CD = 5 and leg CO = 5√3. This must be a 30-60-90 triangle, so the hypotenuse, DO = 10 (aka 5√4)

Return to the Pythagorean Theorem:

EO = 5² + (10)² = √125 = 5√5

FO = 5² + (5√5)² =√150 = 5√6

GO = 5² + (5√6)² = √175 = 5√7

Do you notice a pattern? If we added three more triangles to this series, what would be the measure of the hypotenuse OJ?

Do you have a question to ask the math teacher? Our math teacher, Mary Lou loves puzzles and riddles! Please send your request to info@mytutorlesson.com You just may see it posted here on a future date.