Pythagoras Theorem
What is the formula for the Pythagorean Theorem?
a2+b2=c2
What is required for two triangles to be similar?
What does it mean for two shapes to be similar?
the ratio of corresponding sides is equal and the corresponding angles are equal.
or
Similar shapes are therefore identical in shape, but they differ in size.
What does it mean for two shapes to be congruent?
Congruent shapes are shapes that are exactly the same.
corresponding sides are equal in length, corresponding angles are equal, the shapes have the same area
In a right-angled triangle, if one leg is 3 and the other is 4, what is the length of the hypotenuse?
5
In similar triangles, if one side of a triangle is 4 cm and the corresponding side of a similar triangle is 6 cm, what is the scale factor?
2:3
If a rectangle has dimensions 5x10, what would be the dimensions of a similar rectangle with a scale factor of 3
15 x 30
How many pairs of corresponding angles and sides of congruent triangles are equal?
3
If the hypotenuse of a right triangle is 10 and one leg is 6, what is the length of the other leg?
8
In similar triangles, if one side of a triangle is 24 cm and the corresponding side of a similar triangle is 6 cm, what is the scale factor?
4:1
In similar shapes, if one side of a shape is 6 cm and the corresponding side of a similar shape is 9 cm, what is the scale factor?
2:3
In congruent shapes, if one side of a triangle measures 5 cm, what is the length of the corresponding side in another congruent triangle?
5 cm
A ladder is leaning against a wall forming a right triangle with the ground. If the ladder is 15 feet long and the distance from the base of the ladder to the wall is 9 feet, how high on the wall does the ladder reach?
12
If the scale factor of two similar triangles is 1:3, and one side of the larger triangle is 12 cm, what is the length of the corresponding side in the smaller triangle?
4
Two similar cubes A and B have sides of 15 cm and 5 cm respectively. What is the ratio of their volumes?
27 : 1
If two angles of one triangle are congruent to two angles of another triangle, and 1 side of one triangle to the corresponding side of another triangle, What type of the congruence condition is satisfied?
ASA (Angle Side Angle)
In a right triangle, if the lengths of two legs are 5 and 12, what is the length of the hypotenuse?
13
Given triangle A and Triangle B, the length of the two sides of triangle A is 7 cm and 3 cm.
The the length of the two sides of triangle B that corresponding to triangle A is 28 cm and a cm.
What is the value of a?
12
If two similar triangles have a scale factor of 1:4 and the area of the larger triangle is 80 cm², what is the area of the smaller triangle?
5 cm2
If two rectangles are congruent and one has a length of 8 cm, what is the length of the corresponding side in the other rectangle?
8 cm