| A | B |
|---|
| What is acute triangle? | An acute triangle whose angles are all less than 90 degrees |
| What is a right triange? | A right triangle that has one angle that equals 90 degrees. |
| what is a obtuse triangle? | A obtuse triangle is a triangle with one angle greater than 90 degrees and less than 180 degrees. |
| how many vertices does a triangle have? | A triangle has three (3) vertices. |
| what is always the sum of all the angles of a triangle? | the sum of any triangle is always 180 degrees! |
| In order to construct a triangle what rule must be applied? | the rule is the following; "the sum of the lengths of any two sides must be greater than the third side". For example; If two sides of a triangle add up to 9 inches then the third side has to be greater than 9 inches to construct it. |
| what is the DISTANCE FORMULA? | D= sqrt ( x2 - x1)^2 + ( y2-y1)^2 |
| what is the MIDPOINT FORMULA? | midpoint formula= ( x1 + x2/2) , ( y1 + y2/2) |
| What is the shortest distance between two points? | A "straight line" |
| What is an ISOSCELES TRIANGLE? | A triangle with two equal sides and two equal base angles. |
| What is a SCALENE TRIANGLE? | A triangle with no equal sides, and no equal base angles. |
| what is an EQUILATERAL TRIANGLE | A triangle that has three equal sides and three equal angles. |
| what is an EQUIANGULAR TRIANGLE? | A triangle with just three equal angles. |
| what is a coordinated pair? | It is a point on a graph with an "x" and "y" value. |
| what is the x value of a coordinated pair called? | Domain |
| what is the y value of a coordinated pair called? | range |
| What are "perpendicualar lines"? | Perpendicular lines are lines that intersect at exactly 90 degrees! |
| what are parallel lines? | parallel lines are lines that travel in the same direction and never intersect! |
| what is a Right Scalene triangle? | a triangle with NO equal sides, and ONE angle equals 90 DEGREES! |
| what is a obtuse isosceles triangle? | a triangle with TWO EQUAL sides, and TWO EQUAL base angles, and has one angle that is greater than 90 degrees and less than 180 degrees! |
| what is the point of origin on a graph | (0,0) |
| What two things do you look for in classifying a triangle? | Sides and angles |
| Steps on how to construct "Perpendicular lines"... | 1) Draw a lines segment 2) From intersection point on the line segment draw two arcs 3) where the two arcs cross the line segment put a point 4) Place compass on each of these two points and draw arcs above and below the lines segment 5) Where both arcs crose above and below the line segment connect the points with a straightedge so the line intersects the original line segment 6) Where they intersect on the original line segment are right angles |
| Steps in constructing an acute triangle- | 1) Place the compass where two lines intersect that are perpendicular to each other 2) Draw an arc iin the first quadrent after placing the compass on the perpendicular intersection 3) Place a point anywhere on the arc from 0-89 degrees and then place another point on the line segments to the right of that point on the arc 4) Then with a straightedge connect where the two lines are perpendicular with the point on the arc and then connect with a straightedge and the point on the arc and the point made on the line segment 5) After connecting these three points or vertices one now has an acute triangle. |
| Steps in constructing a right triangle- | 1) Make a point on the line somewhere above the point where the two lines cross that are perpendicular 2) Place a point on the line to the right of the perpendicular intersection 3) With a striaghtedge connect thos two points 4) One will now have a rght triangle |
| Steps in constructing a Obtuse triangle- | 1) Place the compass at the perpendicular intersection of the two line segments and draw an arc in quadrent two 2) Plce a point anywhere on the arc from 90-179 degrees 3) Place a point on the horizontal lines segment in quadrent one 4) With a straightedge connect the point in quadrent two with the point where the two perpendicular line segments intersect and with the straightedge connect the point on the arc in the 2nd quadrent with the point on the horizontal lines segment in quadrent one 5) One now has an obtuse triangle |
| Steps in constructing a "Scalene Triangle"- | 1) Draw a line segment 2) Put a point between th two ends of the line segment 3) Place your compass on that point & construct an arc from one end of line segment to the other 4) Place a point outside of the arc and place one point on the arc 6) Connect all three points 7) This will be a scalene triangle |
| Constructing an isosceles triangle- | 1) Draw a line segment 2) Put a point on the line segment 3) Place compass on that point and construct an arc from one side of line segment to the other side 4) Place two points on the arc 5) Connect all three points together 5) It will be an Isosceles Triangle |
| Constructing an Equilateral and Equiangular Traingle- | 1) Creat a line segment 2) Mark endpoints 3) Place compass at one end point and make it equal to the length of the arc 4) Create an arc above the line segment using the same width 5) Without changing length of the compass place on the opposite endpoint and create an arc above the line segment 6) Place a point where the two arcs intersect 7) Then connect the three points 8) There will be an equilateral equiangular triangle |
| How many degrees will each angle of an Equiangular triangle measure? | They will measure 60 degrees each |
| Is an Equilateral Triangle also an equiangular triangle? | Yes, an Equilateral triangle also has 3 equal angles besides 3 equal sides; Therfore an Equilateral Triangle is also an equiangular triangle |
| Definition: Median- | A median is a line segment from one of the vertices of a triangle to the opposite side, dividing the opposite side into two congruent parts. |
| Definition: Altitude- | AN Altitude is a line segment from one of the vertices of a triangle to the opposite side, forming a right angle or perpendicular intersection. |
| Definiton: Angle Bisector- | An Angle Bisector is a line segment from one of the vertices of a triangle, dividing the angle at the vertex into two congruent parts. |
| Definition: Orthocenter- | It is the point where all the Altitudes of a triangle connect. |
| Where is the orthocenter in an acute triangle? | It is on the inside of the triangle. |
| Where is the orthocenter on a right triangle? | It is on the right angle, directly on the triangle. |
| Where is the orthocenter on a obtuse triangle? | It is outside of the obtuse triangle. |
| What do we know if there is no orthocenter? | We have no triangle. |
| Definition: Centroid- | It is the point where the three medians of a triangle intersect eachother. |
| Definition: Incenter/Point of Concurrency- | The intersection of all the angle bisectors of a triangle. |
| Definition: Circumcenter- | The point in a triangle where the three perpendicular bisectors intersect. |
| How do you calculate the distance of a median using the centroid? | It is 2/3's from the vertex to the centroid, leving 1/3 of the median left. |
