📐 geometry

1. The problem asks to find 5 squares shaded on a 3x3 grid numbered 1 to 9 such that the pattern has 4 lines of symmetry. 2. The 4 lines of symmetry in a square grid are: vertical,

1. **State the problem:** We need to find the order of rotational symmetry of a 5x5 grid pattern with grey squares at positions (1,2), (1,4), (2,3), (3,2), (3,4), (4,2), and (4,4).

1. The problem involves comparing two similar triangles and their corresponding side lengths. 2. Similar triangles have proportional sides, meaning the ratios of corresponding side

1. **State the problem:** We have two similar pentagons ABCDE and RSTUV. We know some side lengths of ABCDE and one side length of RSTUV (TU = 33 cm). We need to find the length of

1. **Circle Theorem Problem:** State the problem: In circle $O$, chord $AB$ subtends an angle of $40^\circ$ at point $C$ on the circumference. Find the angle subtended by the same

1. **Problem statement:** In a circle with center O, points A, B, C, and D lie on the circumference. Chord AB is drawn and angle ACB is formed at point C on the circle. Given that

1. The problem states two scenarios involving quadrilateral ABCD with given angles and parallel lines. 2. We will solve the first scenario: AB || DC, \(\angle BDC = 35^\circ\), and

1. **Problem Statement:** Find the value of $x$ in the parallelogram $ABCD$ where angle $B$ is $34^\circ$ and angle $D$ is $x$.

1. The problem shows a parallelogram ABCD with sides AB and CD opposite each other, and sides AD and BC opposite each other. 2. In a parallelogram, opposite sides are equal in leng

1. The problem states that the angle of 78 degrees is angle PBA, not angle PBO. 2. To clarify, angle PBA means the angle formed at point B by points P and A.

1. **Problem statement:** We are given a circle with center O, points A and B on the circumference, and a tangent line at point B. The angle between line OB and the tangent line PB

1. **State the problem:** We have three triangles sharing a vertex P with some known and unknown angles. We need to find all missing angles, identify which two triangles can form a

1. **State the problem:** We are given a triangle with angles expressed as $3x - 5$, $5y - 4$, and $y + 12$. We need to find the values of $x$ and $y$. 2. **Recall the triangle ang

1. The problem asks to find the values of angles $y$ and $z$ in triangle $UVT$ where the angle at vertex $T$ is $45^\circ$. 2. Recall that the sum of interior angles in any triangl

1. **Problem 1: Find $x$ and $y$ in trapezoids QUIK and SLOW** Given trapezoids QUIK and SLOW with sides and angles:

1. **State the problem:** We have a right triangle with hypotenuse $66$ ft, base $58$ ft, and height $h$ ft. We need to find the missing height $h$. 2. **Formula used:** In a right

1. **State the problem:** We have a right triangle with one leg of length 15 m, a hypotenuse of length 20 m, and the other leg labeled as $a$. We need to find the length of $a$. 2.

1. The problem is to create the silhouette of a dog on a coordinate plane with $x$ and $y$ values ranging from $-6$ to $6$. 2. To do this, we need to understand that a silhouette c

**Step 1:** Imagine your room is a rectangle shape. 🏠 **Step 2:** To find the area, you multiply the length by the width. 📏 ➕ 📏

1. **State the problem:** Determine which triangles are similar to triangle $\triangle ABC$ with sides $3$, $7$, and $7$. 2. **Recall similarity criteria:** Triangles are similar i

1. **State the problem:** We need to determine which triangles are similar to triangle $\triangle ABC$ with sides $AB=36$, $BC=32$, and $CA=24$. The candidates are $\triangle DEF$