The document provides instruction on classifying triangles and the Pythagorean theorem. It defines right triangles as having one 90 degree angle and defines the legs and hypotenuse. It presents the Pythagorean theorem that the sum of the squares of the two legs equals the square of the hypotenuse. It also provides corollaries that an acute triangle has the sum of the leg squares less than the hypotenuse square, an obtuse triangle has the sum greater than the hypotenuse square, and a right triangle has the sums equal. It asks students to classify triangles as acute, obtuse or right using the corollaries and Pythagorean theorem.
This question tests concepts of finding areas of semi circles and right isosceles triangles. The crux of solving this GMAT problem solving practice question is one's ability to see the shaded region and the remaining parts as geometrical shapes for which areas can be computed.
Presented as part of Q-51 series by 4GMAT. Tough GMAT Quant practice questions.
Area of focus: Trigonometry and mathematical proofs
Topics covered:
> Trigonometry
> Right triangle definitions
> Trigonometric functions
> Special right triangles
> Law of sines
> Law of cosines
> Postulates and axioms
> Theorems
> Pythagorean Theorem
> Mathematical proof
Suggested time to complete (2 hrs):
> Teaching material (40 minutes)
> Practice activity (20 minutes)
> Final project (60 minutes)
Difficult GMAT Geometry Data Sufficiency - Q51 Seriesq51
This one is a data sufficiency question. Concept tested is to figure out whether the data presented is sufficient to determine the dimensions of a triangle and therefore compute its area. Such concepts are often tested in the GMAT quant section.
a, b, and c are sides of a right triangle. What is the area of the triangle?
Statement 1 : a = 4
Statement 2 : a + b + c = 12q
This question tests concepts of finding areas of semi circles and right isosceles triangles. The crux of solving this GMAT problem solving practice question is one's ability to see the shaded region and the remaining parts as geometrical shapes for which areas can be computed.
Presented as part of Q-51 series by 4GMAT. Tough GMAT Quant practice questions.
Area of focus: Trigonometry and mathematical proofs
Topics covered:
> Trigonometry
> Right triangle definitions
> Trigonometric functions
> Special right triangles
> Law of sines
> Law of cosines
> Postulates and axioms
> Theorems
> Pythagorean Theorem
> Mathematical proof
Suggested time to complete (2 hrs):
> Teaching material (40 minutes)
> Practice activity (20 minutes)
> Final project (60 minutes)
Difficult GMAT Geometry Data Sufficiency - Q51 Seriesq51
This one is a data sufficiency question. Concept tested is to figure out whether the data presented is sufficient to determine the dimensions of a triangle and therefore compute its area. Such concepts are often tested in the GMAT quant section.
a, b, and c are sides of a right triangle. What is the area of the triangle?
Statement 1 : a = 4
Statement 2 : a + b + c = 12q
These slides contain the pathagorean theorem and right trinagles. How to prove the oathagorean theorem and how to vind the area of triangles by the pathagorean theorem. There are some slides that explains that how the pathagorean theorem was discovrers. Some slides explain the pathagorean triple theorem and c^2=a^2 + b^2.
1. Geometry drill 1/8/13
Warm Up
Classify each triangle by its angle measures.
1. 2.
acute right
3. Simplify 12
4. If a = 6, b = 7, and c = 12, find a2 + b2 and find c2.
Which value is greater?
85; 144; c2
2. Objective
SW define and apply the
Pythagorean Theorem
so that they can find the
dimensions of geometric
figures.
12. Corollary to the
Pythagorean
Theorem
If the sum of the squares
of the two shorter sides
of a triangle is less than
the square of the longest
side, then the triangle is
______.
13. Corollary to the
Pythagorean
Theorem
If the sum of the squares
of the two shorter sides
of a triangle is less than
the square of the longest
side, then the triangle is
______.
obtuse
14. Corollary to the
Pythagorean
Theorem
If the sum of the squares
of the two shorter sides
of a triangle is greater
than the square of the
longest side, then the
triangle is ______.
15. Corollary to the
Pythagorean
Theorem
If the sum of the squares
of the two shorter sides
of a triangle is greater
than the square of the
longest side, then the
triangle is ______.
acute
16. Corollary to the
Pythagorean
Theorem
If the sum of the squares
of the two shorter sides
of a triangle is equal to
the square of the longest
side, then the triangle is
______.
17. Corollary to the
Pythagorean
Theorem
If the sum of the squares
of the two shorter sides
of a triangle is equal to
the square of the longest
side, then the triangle is
______.
right