How to find the hypotenuse
The hypotenuse is the longest side of a right triangle. It is the side that is opposite the 90º angle of the triangle. The length of the hypotenuse can be found using the Pythagorean theorem, which states that the squares of the two shorter sides is equal to the square of the hypotenuse.
a2 +
b2 =
c2
For example, if the sides of a right triangle are 3, and 4, then 9 + 16 = 25. The length of the third side is the square root of 25 which is 5.
Task 11
Geometry Challenges
1. If a right triangle has a side of 5 inches, and a hypotenuse of 13 inches, how long is the third side?
2. A runner runs diagonally across a football field that is 40 yards long and 30 yards wide, how far does the runner run?
3. A playground slide is 17 feet long, and travels 15 feet along the ground. What is the height of the ladder to the top of the slide (assume all sides are straight)?
Enjoy yourself!
Farmer Giles has four sheep. One day, he notices that they are standing in such a way that they are all the same distance away from each other. That is to say, the distance between any two of the four sheep is the same. How can this be so?
The sheep are standing on the four corner points of an equal-sided pyramid (a tetrahedron). Or to put it another way, three are on the points of an equilateral triangle and the other is on a mound of earth in the center.
Self-assessment
Be ready to speak on the topic "Simple closed figures" using the following as a plan:
What does geometry study?
What are the main geometric notions?
What is a point?
What does a line consist of?
What does a line form?
What does a line segment include?
What is a ray?
How can we get an angle?
What do we call a vertex of the angle?
How does the angle separate the plane?
What is a polygon?
What does a polygon consist of?
How can polygons be classified?
What is a triangle?
What types of triangle do you know?
What triangle do we call an equilateral one?
What is an isosceles triangle?
How do we call the sides of the right triangle?
What is a quadrilateral?
How do we call the parallel sides of a trapezoidal?
Check your active vocabulary on the topic:
a simple closed figure in the space on the plane exact location a ray an angle to extend direction a common point
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interior, exterior right, acute, obtuse angle degree measure linear measure side boundary to enclose, to intersect a polygon right,equilateral, isosceles triangle |
the vertex of the angle a leg a hypotenuse opposite parallelogram quadrilateral trapezoidal a base of trapezoidal |
Translate into English and be ready to give illustrative examples:
оточувати, вміщати, перетинати проста замкнена фігура вершина кута точне розташування поширюватися промінь кут напрям трапеція
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основа трапеції прямокут., рівностор., рівнобедр. трикутник катет та гіпотенуза чотирикутник багатокутник паралелограм прямокутник |
прямий, тупий, гострий кути кордон, межа градусна міра міра сторін, їх довжина сторона внутрішній, зовнішній у просторі спільна точка на площині
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Fill in the gaps using a word from the list:
interior sets obtuse hypotenuse geometric |
right Vertex boundary between plane |
ray angles acute quadrilateral point |
Geometry studies figures in the space and on the … .
The main … ideas are the ideas of a point and a line.
A … is an exact location in space.
A line consists of … of points.
Lines form line segments, rays and ….
A line segment includes endpoints and all points … them.
A … is a line segment extended in one direction.
The common point of the two rays is the … of the angle.
Angles separate the plane into three distinct sets of points: …, exterior, and the angle.
A … angle has a measure of 90°.
An … angle has a degree measure less than 90°.
An … angle has a degree measure greater than 90°.
A simple closed figure is any figure drawn in a plane in such a way that … never crosses or intersects itself and encloses part of the plane.
A … is a side opposite to the right angle.
A parallelogram is a … whose opposite sides are parallel.
MODULE 7