📐 geometry

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 $\triangle DEF$

1. The problem is to understand whether to multiply or add when dealing with a cuboid. 2. A cuboid is a three-dimensional shape with length ($l$), width ($w$), and height ($h$).

1. **Problem statement:** A cyclist starts from point X, rides 3 km due west to point A, then rides 5 km northwest to point Z. We need to find:

1. **State the problem:** Find the surface area of a pyramid with a triangular base where each base edge is 10 units and the slant height is 12 units. 2. **Formula for surface area

1. **State the problem:** We have a triangle with sides 5.2 cm, 6.3 cm, and 9.4 cm, each measured to the nearest millimeter (0.1 cm). We need to find the lower bound of the perimet

1. **Problem Statement:** We have a right-angled triangle $\triangle ACE$ and a square $PQRS$ inside it.

1. **Problem Statement:** Fill in the 6 blanks with the correct triangle congruence statements or "Not Possible" based on the given graphs. 2. **Recall the criteria:**

1. **Problem Statement:** Determine if triangles are congruent by ASA or AAS and match the correct congruence statement. 2. **Recall the criteria:**

1. **Problem Statement:** Given a right-angled triangle \(\triangle ACE\) with \(AB=\frac{40}{3}\), \(BC=10\), \(BR=ER\), and \(\angle BEC=45^\circ\). Points E and F have equal per

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