📐 geometry

1. **Problem Statement:** We have a metal strip composed of five trapezoidal shapes aligned horizontally with a total length of 150 mm and height 20 mm. We need to find the area of

1. **State the order of rotation and angle of rotation for each figure:** - The order of rotation is the number of times a figure maps onto itself during a full 360° rotation.

1. **Problem statement:** Given a right triangle ABC with a right angle at A, AC = 27 cm, BC = 45 cm, and AB = 3x cm. Find the value of $x$. 2. **Formula used:** In a right triangl

1. The problem asks us to find the coordinates of the vertices E, F, G, and H after a 180° counterclockwise rotation about the origin. 2. The original coordinates are:

1. **Problem statement:** Given a right triangle ABC with right angle at A, AC = 27 cm, BC = 45 cm, and AB = 3x cm, find the value of $x$. 2. **Formula used:** Pythagorean theorem:

1. **Problem Statement:** We are given a triangle \(\triangle PQR\) with vertices \(P(5,6)\), \(Q(6,7)\), and \(R(4,8)\). We want to find the coordinates of the image of \(\triangl

1. **Problem Statement:** We are given a triangle PQR with vertices at points $P(3,6)$, $Q(4,8)$, and $R(2,9)$. We need to find the coordinates of the triangle after translating it

1. **Stating the problem:** We need to find the volume of a trapezoidal prism with given side lengths. 2. **Formula for volume of a prism:**

1. Let's identify the problem: We need to find the missing lengths of two triangles, one purple and one rusty looking, presumably right triangles. 2. The key formula for right tria

1. **Problem Statement:** Find the hypotenuse of the top right-angled triangle with legs 5 cm and 5 cm. Also, find all missing lengths of the stacked right-angled triangles from bo

1. **Problem statement:** We are given points $P(1,1)$ and $Q(7,11)$ which form the diameter of a circle.

1. **Problem statement:** We have two circles: a smaller circle with center A and radius $r$ passing through points B, C, and D, and a larger circle with center C and radius $s$ pa

1. **Problem Statement:** Quadrilateral ABCD is dilated to form quadrilateral EFGH. We are given side lengths of ABCD as 8 (CB) and 10 (BA), and corresponding side lengths of EFGH

1. **Problem Statement:** Given that triangles $\triangle ABC$ and $\triangle MNP$ are similar, determine which of the following statements is true: I. $\frac{AC}{BC} = \frac{MP}{N

1. **פתרון תרגיל 1:** א. נתונות משוואות הצלעות AB ו-CD בטרפז:

1. **Problem Statement:** Given quadrilateral ABCD with point O inside it, and points W, X, Y, Z as midpoints of segments AO, BO, CO, and DO respectively, prove that quadrilateral

1. **Stating the problem:** We need to find the size of the angle $\alpha$ in the given geometric configuration involving a rectangle, two circles (one smaller with radius $r$ and

1. **Stating the problem:** We have two parallel lines "a" and "b" cut by a transversal. The angle adjacent to the transversal on line "a" is $3x + 30^\circ$ and the corresponding

1. **Stating the problem:** We have a mobile login screen layout composed of geometric shapes with given vertices:

1. **State the problem:** We have a parallelogram KLMN with angles at vertices N and L given by $7x - 30^\circ$ and $5x + 18^\circ$ respectively. We need to find the value of $x$ a

1. **Problem Statement:** We have a parallelogram KLMN with angles at vertices L and N given by $5x + 18^\circ$ and $7x - 30^\circ$ respectively.