📐 geometry

1. The problem asks to find the translation rule that maps triangle BCD to triangle B'C'D'. 2. The translation rule is generally written as $$(x, y) \mapsto (x + a, y + b)$$ where

1. **State the problem:** We need to find the area of a right triangle with one leg measuring 60 mm and the other leg measuring 21 cm. 2. **Convert units to be consistent:**

1. **State the problem:** We need to find the perimeter of a right-angled triangle with legs measuring 3 m and 14 m. 2. **Formula used:** The perimeter $P$ of a triangle is the sum

1. **State the problem:** We need to find the perimeter of a right-angled triangle with one leg measuring 3 m and the hypotenuse measuring 14 m. The other leg length is unknown. 2.

1. **Problem statement:** We have triangle $\triangle ABC$ with vertices $A(1,-3)$, $B(-2,-2)$, and $C(-1,0)$. The triangle is translated by $+5$ units in the x-direction and $-4$

1. **State the problem:** We have a triangle with two known angles 57° and 60°, and two unknown angles $x$ and $y$ adjacent to the triangle on a straight horizontal line. We need t

1. **Stating the problem:** We have a right-angled triangle with sides 3 m, 4 m, and 5 m. We want to find the sum of the two non-right angles (a).

1. **State the problem:** We need to find the length of the hypotenuse $h$ of a right-angled triangle with legs measuring 12.34 m and 15.2 m. 2. **Formula used:** According to the

1. **State the problem:** We need to find the circumference of a circle with a diameter of 16.2 cm. 2. **Formula:** The circumference $C$ of a circle is given by the formula:

1. The problem asks to find the circumference of a circle with a diameter of 132 cm. 2. The formula for the circumference $C$ of a circle is:

1. **State the problem:** We have a triangle with angles measuring $32^\circ$, $(7a + 4)^\circ$, and $(3(b + 2) - 1)^\circ$. We need to find the values of $a$ and $b$. 2. **Recall

1. The problem asks to locate the point $(-1.6, -1)$ on the Cartesian coordinate plane and identify its position relative to the axes or quadrants. 2. Recall that the Cartesian pla

1. **State the problem:** Find the unknown segment lengths indicated by "?" in two tangent-secant configurations involving circles.

1. **State the problem:** Find the perimeter of each polygon given the side lengths. 2. **Recall the perimeter formula:** The perimeter $P$ of a polygon is the sum of the lengths o

1. **State the problem:** We have a right triangular prism with a base triangle having legs 5 in and 9 in, and height 12 in. We need to find: (a) The length $a$, which is the hypot

1. **State the problem:** We have a convex pentagon with interior angles 82°, 121°, 129°, 147°, and an unknown angle $x$. We need to find $x$. 2. **Formula used:** The sum of inter

1. The problem is to find the angle corresponding to the second half of 2 in a triangle context. 2. Assuming the problem refers to dividing an angle of 2 radians into two equal par

1. **Problem 19:** Find the area of the shaded region inside a circle with radius 6. 2. The formula for the area of a circle is $$A = \pi r^2$$ where $r$ is the radius.

1. **State the problem:** We need to find the measure of angle $\angle MPQ$ given two expressions for angles formed by a transversal intersecting two parallel lines. 2. **Identify

1. **State the problem:** We are given two angles formed by a transversal intersecting two parallel lines. The angles are \( (12x - 23)^\circ \) and \( (71 - x)^\circ \). We need t

1. The problem asks which quadrilateral has at least one pair of perpendicular sides. 2. Perpendicular sides meet at a right angle, which is $90^\circ$.