📐 geometry

1. **State the problem:** We are given a triangle with points B, K, C, L, and D. Segments BK = 10, KC = 5, BL = 13, and LD = y. We need to find the length of segment LD, denoted as

1. **Problem statement:** We are given a geometric figure with points B, K, C, L, and D. The segments BK = 10, KC = 5, BL = 13, and LD = y. We need to find the length y. 2. **Under

1. The problem asks if the lighter colored quadrilateral is a dilation of the smaller quadrilateral. 2. A dilation means the shapes are similar: all corresponding angles are congru

1. **Problem Statement:** Given that ABCD is a parallelogram, determine which of the following statements are NOT true: - Diagonals are congruent in length

1. **Problem 1A: Reflecting point P over the x-axis** The original point P is at coordinates $P(3,5)$. When reflecting a point over the x-axis, the x-coordinate remains the same, b

1. **State the problem:** Calculate the surface area of the attic given by the expression $$45 (40 + 25 + 25) + \frac{1}{2} (40 \times 15)$$. 2. **Understand the formula:** The exp

1. **State the problem:** We need to determine which shortcut can be used to prove that the two right triangles shown are congruent. 2. **Identify given information:** Both triangl

1. **State the problem:** Find the distance between each pair of points given. 2. **Formula used:** The distance $d$ between two points $(x_1, y_1)$ and $(x_2, y_2)$ in the plane i

1. The problem asks to complete the drawings using the line of symmetry marked by the dashes. 2. A line of symmetry means that one side of the shape is a mirror image of the other

1. **Problem Statement:** Given two wedges joined together, find the resultant wedge angle or combined effect.

1. **Problem statement:** In rectangle MNPQ, one vertex lies on the circle, and two vertices lie on the diameter of the circle. Given $MN=4$ and $MQ=6$, find $QL$. 2. **Understandi

1. The problem states the Pythagorean theorem: $x^2 + y^2 = z^2$. 2. This formula relates the lengths of the sides of a right triangle, where $x$ and $y$ are the legs and $z$ is th

1. **State the problem:** We need to determine which information can be used to prove that triangle ABC is congruent to triangle DEF. 2. **Given information:**

1. The problem asks to find the area of a shape with given dimensions 5, 4, and 1 square units. 2. Since the problem does not specify the shape, we assume it is a rectangle or a co

1. **State the problem:** Find the area of a parallelogram with base $7$ cm and height $3$ cm. 2. **Formula:** The area $A$ of a parallelogram is given by the formula:

1. **Problem Statement:** Construct triangle PQR where $PQ=4.5$ cm, $QR=5.2$ cm, and angle $PQR=45^\circ$. 2. **Formula and Rules:** To construct a triangle given two sides and the

1. **State the problem:** Find the distance between points $A(2,5)$ and $B(4,9)$ using the distance formula. 2. **Distance formula:** The distance $d$ between two points $A(x_1,y_1

1. **Problem statement:** Find the length of the side marked $x$ in each right triangle given the angle and one side. 2. **Key formulas and rules:**

1. **Problem statement:** We have a square-based pyramid with base ABCD where side AD = 19 cm.

1. **Problem statement:** We need to find the length of segment $HD$ in the given geometric figure with points $O, H, P, D, I$ and given lengths $OH=6$, $PD=9$, and $PI=27$. 2. **U

1. **Problem statement:** Given points A(2,3), B(-1,-4), and C(0,-2), find: a. The distance |AB|