📐 geometry

1. The problem is to find the values of angles that sum to 180 degrees. 2. The key formula is that the sum of angles in a triangle is always $$180^\circ$$.

1. The problem asks: What is a rectangle? 2. A rectangle is a type of quadrilateral (a four-sided polygon) where all interior angles are right angles (each measuring 90 degrees).

1. The problem asks to find the area of an irregular U-shaped polygon with given side lengths. 2. To find the area, we divide the shape into smaller rectangles.

1. Problem: Find the area of a rectangle with length $l=8$ and width $w=5$. 2. Formula: The area $A$ of a rectangle is given by

1. **Problem statement:** Given three lines AB, EF, and CD intersecting at point O, with AB perpendicular to CD, and the ratio of angles $m\angle 1 : m\angle 2 = 1 : 2$, find $m\an

1. **Problem statement:** We have a rectangle ABCD with sides 6 and 4. The paper is folded so that vertex A lies on side BC. We need to find the area of the shaded triangle EAD. 2.

1. The problem is to find the area equations for common 2D shapes. 2. The area of a shape is the amount of space inside its boundary.

1. **State the problem:** We have triangle ABC with points A(2,3), B(7,1), and C(1,1). It is enlarged about the origin with a scale factor of $-2$ to form triangle A'B'C'. We need

1. **State the problem:** We have two parallel slanted lines crossed by a horizontal transversal. The angles labeled are $9x^\circ$ (below the transversal, right of the left slante

1. **State the problem:** We need to find the size of angle $k$ in a quadrilateral-like shape where two sides are parallel and two segments are equal in length. 2. **Identify given

1. **Problem statement:** We have triangle $\triangle RPT$ inscribed in circle $\odot P$ with center $P$. Points $R$ and $T$ lie on the circle, and the measure of arc $RT$ is given

1. **State the problem:** We have a prism with a square cross-section of side 13 cm and depth 5 cm. There is a circular hole through the prism with diameter 6 cm. We need to find t

1. **State the problem:** We are given three intersecting lines forming angles around a point. Two angles are given: 77° and 70°, and we need to find the value of angle $w$. 2. **R

1. **State the problem:** Find the area of a parallelogram with base length 13 yd and height 9 yd. 2. **Formula:** The area $A$ of a parallelogram is given by

1. The problem asks to find the area of a circle with diameter 8 ft, using \(\pi = 3.14\) and no rounding. 2. The formula for the area of a circle is:

1. **State the problem:** We have a floor plan with a scale of 2 cm : 5 m.

1. **State the problem:** We have two similar quadrilaterals. The smaller one has side lengths 3 inches and 1 inch, and the larger one has corresponding side lengths 2 inches and a

1. The problem asks to complete the congruence statement between triangles \(\triangle GHI\) and \(\triangle MNL\).\n\n2. Given the markings: \n- In \(\triangle GHI\), angle \(G\)

1. **State the problem:** Find the surface area of a triangular prism with triangle side lengths 5 ft, 12 ft, and 13 ft, and prism length 6 ft. 2. **Formula for surface area of a t

1. **State the problem:** We have a large rectangle with width 7 yd and height 14 yd. A smaller rectangle of height 3 yd is removed horizontally near the top, creating two shaded r

1. **Problem Statement:** We are given two triangles, GHI and RST, with the following congruences: \(\angle G \cong \angle R\), \(\angle H \cong \angle S\), and segment \(GI \cong