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I can classify triangles by side lengths - scalene, isosceles, equilateral

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I can classify triangles by side lengths - scalene, isosceles, equilateral

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The sum of angle measures in triangles is 180

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The sum of angle measures in triangles is 180

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Similar triangles are same shape different size

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Similar triangles are same shape different size

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I can solve for segment lengths using proportions

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I can solve for segment lengths using proportions

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This only works for similar right triangles

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This only works for similar right triangles

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Range of possible values for an unknown side of a triangle can be found by subtracting the other sides from each other and the max is determined by adding the 2 sides together.

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The 2 smallest sides of a triangle must add up to more than the length of the longest side.

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Triangle Sum Theorum
Exterior Angle Theorum
Base Angles Theorum
Finding Angles and Lines
If two lines in a triangle are congruent, the angles are too
Proofs of triangles

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Types of triangles iscoles at least 2 sides are congruent. Scalene no sides are congruent. Equilateral all 3 sides are congruent.

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Types of triangles iscoles at least 2 sides are congruent. Scalene no sides are congruent. Equilateral all 3 sides are congruent.

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When all sides are congruent it’s an equilateral triangle

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the sum of any two sides must be greater than the third

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How to classify triangles by angles, acute right and obtuse, based on Pythagorean theorem. Also how we classified by sides, scalene isosceles and equilateral. How to know what side lengths will make a triangle.

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The sum of any 2 sides must be greater than the third and those correspond to the angles and side lengths where the longest side is the largest angle and the shortest side is the shortest angle.

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Triangles have 3 sides. The sum of any two sides must be greater than the measure of the third side in order to make a triangle. Isosceles have two congruent sides. Scaelene have no congruent sides. Equilateral have 3 congruent sides. Triangles can also be classified by angle measures (acute and obtuse.

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Triangles can be classified by angle (acute, right, or obtuse), and by side properties (scalene, isosceles, or equal lateral)

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I learned the different types of triangles
Like iscoles have two congruent sides and the biggest angle is looking always at the biggest side
In the scalene no side are congruent
And you can identify a right triangle with pytagorean  theorem

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There area acute triangles which is c^2< a^2 + b^2

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There area acute triangles which is c^2< a^2 + b^2

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Then right triangles c^2= a^2+ b^2
Then obtuse triangles c^2> a^2 + b^2

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The two smallest sides sum must be greater then the third side for it to be a triangle.

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measure of angle 1 + measure of angle 2 > measure of angle 3

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Exterior Angles can help you find the inside angels.

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Lonest side is opposite of largest angle and shortest side is opposite of shortest angle

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the two smaller sides must add up to be greater than the longest

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Scalene has no congruent sides

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If you have an isosceles triangle then base angles are congruent then sides are congruent

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Triangle sum theorem, which is that all the angles in a triangle add up to 180 degrees. Also we learned exterior angle theorem, which is how you can use an angle outside the triangle to find angles that are inside the triangle. The last thing was base angles theorem which basically means (for isosceles) that if 2 sides are congruent then those 2 angles are congruent. We did proofs

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The line across from the smallest angle is the shortest line

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all angles add up to 180°

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Exterior Angles are angles that are outside of the triangle. The angle also needs to share a side with the triangle.

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Longest side across to longest side, shortest side to shortest side 

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Longest side across to longest side, shortest side to shortest side 

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Triangle angles always add up to 180 and the add up of two and are the exterior angle of the angle you didn’t use

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The sum of all interior angles equal 180°

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Equilateral- all equal sides
Isosceles- 2 equal sides
Scalene- no equal sides
A cute
Obtuse
Right

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We proved that the exterior angle equals the sum of the adjacent 2 angles

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The sum of the measures of interior angles  add up to 180.

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All isosceles right triangles are similar

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If you have an isosceles triangle, that is a right anglethe measures of the angles will be 45,45, and 90

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Side A times the square root of 2 is the hypotenuse on a 45 45 90 triangle

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We learned that the hypotenuse is x times the square root of 2

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a square cut in half is an isosceles right and to get to the other parts of the triangles you either divide or multiply by the square root of 2

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It is created by a isosceles right triangle and has a ratio of 1:1: square root of 2

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If the triangle has this set of angles is going to be a isosceles right triangle meaning that it has two congruent sides and a right angle

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Two triangles that form a square the diagonal is 45 45 90

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hyopotinuse is x times square root of 2

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If the legs of a 45-45-90 triangle are length s, then the hypotenuse of the triangle is s times the square root of 2.

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to get the hypotenuse of a isosceles right triangle you multiply a leg by the square root of 2

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The ratios of the sides are one-square root three-two

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The ratios of the sides are one-square root three-two

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Multiply the short leg by two to get the length of the hypotenuse

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Multiply the short leg by two to get the length of the hypotenuse

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Multiply the short leg by square root 3 to get length of long leg

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Multiply the short leg by square root 3 to get length of long leg

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Divide the hypotenuse by 2 to get the short leg

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Divide the hypotenuse by 2 to get the short leg

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Divide the long leg by the square root 3 to get the short leg

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Divide the long leg by the square root 3 to get the short leg

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square root 3 times square root 2 = square root 6

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square root 3 times square root 2 = square root 6

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The AA Theorum, the SSS Theorum, and the SAS Theorum and how the triangle relates to them

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Similar triangles have the same angles and have a proportion so they are the same shape just in a different size

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Similar triangles have the same angles and corresponding sides. You can prove a triangle is similar using two similar angles and three corresponding sides. You can also use one similar angle and two corresponding sides to prove they are similar.

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For a triangle to be similar it must have congruent angles and proportional sides

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similar triangles have same shape,same angle measurements,but different sizes

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similar triangles have the same angle measures but different side lengths

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In similar figures, all corresponding angles are congruent and corresponding sides have equal ratios - they are proportional

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In similar figures, all corresponding angles are congruent and corresponding sides have equal ratios - they are proportional

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The midsegment of a triangle connects the midpoints of two sides

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The midsegment of a triangle connects the midpoints of two sides

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The midsegment is parallel to the third side and half the length of the third side

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The midsegment is parallel to the third side and half the length of the third side

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If three parallel lines intersect two transversals, then they divide the transversals proportionally

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If three parallel lines intersect two transversals, then they divide the transversals proportionally

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If a ray bisects an angle of a triangle, then it divides the opposite side into two segments with lengths proportional to the lengths of the other two sides

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If a ray bisects an angle of a triangle, then it divides the opposite side into two segments with lengths proportional to the lengths of the other two sides

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The geometric mean is in specific positions in a proportion

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The geometric mean is in specific positions in a proportion

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In a right triangle, the altitude from the right angle to the hypotenuse divides the triangle into three similar triangles

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In a right triangle, the altitude from the right angle to the hypotenuse divides the triangle into three similar triangles

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In a right triangle, the altitude from the right angle to the hypotenuse divides the hypotenuse into two segments.

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In a right triangle, the altitude from the right angle to the hypotenuse divides the hypotenuse into two segments.

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The length of the ALTITUDE is the geometric mean of the length of these two segments

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The length of the ALTITUDE is the geometric mean of the length of these two segments

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Each LEG is the geometric mean of the hypotenuse and the segment of the hypotenuse it's adjacent to

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Each LEG is the geometric mean of the hypotenuse and the segment of the hypotenuse it's adjacent to