📐 geometry

1. **Problem 4: Are triangles MNO and XYZ similar?** Given sides:

1. **Problem:** Find the area of each circle in terms of $\pi$. The formula for the area of a circle is: $$\text{Area} = \pi r^2$$

1. **Problem:** Find the area of a circle with radius 15 ft. 2. **Formula:** The area of a circle is given by $$A = \pi r^2$$ where $r$ is the radius.

1. **Problem statement:** We have a circle with center O and a vertical tangent line touching the circle on the right. Inside the circle, there is an angle of 31° formed at the top

1. **Problem (a):** Determine if triangles ABC and FDE are congruent given that AB = FD (one tick) and angles at C and E are marked. 2. **Formula and Rules:** To prove triangle con

1. **State the problem:** We have a right triangle with legs of lengths $9$ and $x$, and hypotenuse length $24$. We need to find the exact value of $x$. 2. **Formula used:** In a r

1. **State the problem:** We have a right triangle with legs of length 8 and $x$, and hypotenuse of length 17. We need to find the exact value of $x$. 2. **Formula used:** In a rig

1. **Problem statement:** We have two circles representing the ranges of transmitters on boats A and B. - Circle A has center A and radius $r_A = 7$ km.

1. The problem is to calculate the area of a circle using $\pi = 3.14$. 2. The formula for the area of a circle is $$A = \pi r^2$$ where $r$ is the radius.

1. **State the problem:** Calculate the circumference and area of a circle with radius $r = 9.5$ inches.

1. **State the problem:** Calculate the perimeter and area of the trapezoid with given side lengths: top base = 42 ft, left side = 30 ft, right vertical sides = 18 ft and 20 ft, an

1. **State the problem:** Calculate the perimeter and area of the given right triangle with sides 20 cm (base), 30 cm (hypotenuse), and a height of 13 cm drawn perpendicular to the

1. **State the problem:** We compare two square pyramids. The first pyramid has height $h_1$ equal to one third its width $w_1$, i.e., $h_1 = \frac{1}{3} w_1$. The second pyramid h

1. **State the problem:** Calculate the area of a right-angled triangle with perpendicular sides of lengths 3 m and 14 m. 2. **Formula:** The area $A$ of a right-angled triangle is

1. **Problem:** Calculate the scale of a map where the distance between Braga and Guimarães is 4 cm on the map, but the real distance is 16 km. 2. **Formula:** The scale of a map i

1. **Problem Statement:** We have a cube net with points labeled and a point X on the right middle square's right edge midpoint. We want to find which two points X meets when the n

1. **State the problem:** We are given a triangle with sides $a=3.6$ cm, $b=7.5$ cm, and $c=5.1$ cm. We need to find the measures of angles $A$, $B$, and $C$. 2. **Formula used:**

1. **State the problem:** We have a right triangle with one leg measuring 1 cm and the hypotenuse measuring 2 cm. We need to find the length of the other leg. 2. **Formula used:**

1. **State the problem:** Find the value of $x$ and determine if the angles are adjacent or vertical. 2. **Exercise 1:** Angles $120^\circ$ and $x^\circ$ are adjacent on a straight

1. **State the problem:** Find the lengths of the legs and the hypotenuse of the right triangle formed by points $(-5, 3)$ and $(-8, 6)$. 2. **Formula used:** The distance between

1. **Problem Statement:** Calculate the areas of Figure A and Figure B based on the given dimensions and verify the statements about their areas.