📐 geometry

1. **State the problem:** You want to know where to place the marks for sides and angles in the diagram to indicate congruence based on the given information. 2. **Given informatio

1. **State the problem:** Given that $\angle G \cong \angle I$ and that $FH$ bisects $\angle GFI$, prove that $\triangle GFH \cong \triangle IFH$. 2. **Write down the given informa

1. The problem asks to find the ratio $n$ between the length of side $DE$ and the length of the corresponding side $AB$. 2. The ratio $n$ is defined as:

1. **State the problem:** We need to dilate triangle $\triangle ABC$ centered at the origin using the scale factor $n$ from part D, then compare the side lengths of the dilated tri

1. **Problem Statement:** Find the area of the irregular polygon with given side lengths: vertical left side 17 yd, horizontal segments 5 yd, 4 yd, 5 yd, 5 yd, bottom base 7 yd, ve

1. Statement of the problem: Find the area of the polygon composed of a right triangle with base 8 km and height 5 km attached to an orthogonal region with labeled sides as describ

1. **State the problem:** Find the area of a composite figure consisting of a large right triangle and two rectangles. 2. **Identify the shapes and their dimensions:**

1. The problem asks to identify the two transformations that show figure ABCD is congruent to figure A'B'C'D'. 2. The original rectangle ABCD has vertices at approximately $(6,6)$,

1. The problem asks to identify the two transformations that show figure ABCD is congruent to figure A'B'C'D'. 2. Given the coordinates:

1. **Problem statement:** Quadrilateral DEFG is a kite with angles at vertices E and G given as $55^\circ$ and $89^\circ$ respectively. We need to find the measure of angle $F$. 2.

1. **Problem statement:** Given kite GHJI with angles at vertices J and H as 76° and 98° respectively, find the measure of angle I. 2. **Recall kite properties:** In a kite, two pa

1. The problem is to find the missing angle in a triangle where two angles are given as 65° and 65°. 2. The sum of the interior angles in any triangle is always 180°. This is a fun

1. **Problem Statement:** We have a line segment with endpoints at $A(2,4)$ and $B(4,2)$. We want to perform a dilation on this segment and find the coordinates of the endpoints af

1. **State the problem:** Two cars start from the same point. One travels north 4 km, the other east 3 km. We want to find the straight-line distance between them. 2. **Formula use

1. **State the problem:** We have three people: Brody, Darrell, and Sandra. Darrell is directly behind Brody and directly left of Sandra. 2. **Given:**

1. **State the problem:** A hummingbird's nest is 12 meters high in a tree, and a flower is 9 meters away from the base of the tree on the ground. We need to find the distance the

1. **State the problem:** A bird is 12 feet from the base of a tree and flies 20 feet to the top of the tree. We need to find the height of the tree. 2. **Identify the right triang

1. **State the problem:** Albert's flour fills a cylindrical jar with diameter 4 inches and height 6 inches. We want to find which containers can hold the same volume of flour. 2.

1. **State the problem:** We need to find the radius $r$ of a cone given its volume $V = 150.72$ cubic millimeters and height $h = 9$ millimeters. 2. **Formula:** The volume of a c

1. **State the problem:** We are given the volume $V = 150.72$ cubic millimeters and height $h = 9$ millimeters of a cone, and we need to find its radius $r$ rounded to the nearest

1. **Problem Statement:** Given two parallel lines $p \parallel q$ cut by a transversal $r$, with $\angle s = 79^\circ$ on line $q$ and $\angle x = 101^\circ$ on line $p$. We need