📐 geometry

1. **Problem:** Show that the points (-2, 10), (3, -2), and (15, 3) are vertices of an isosceles triangle. 2. **Formula:** To check if a triangle is isosceles, calculate the distan

1. The problem is to understand the concept of a ladder, which is typically a tool used to climb to higher places. 2. A ladder can be described mathematically in problems involving

1. **Problem statement:** Given that triangles $\triangle ABC$ and $\triangle PRQ$ are similar, find the unknown values $x$ (angle $Q$) and $y$ (side $BC$). 2. **Similarity rules:*

1. **State the problem:** We need to find the length of side $SR$ in triangle $PSR$, which is isosceles with $PS = SR$. Given $PR = 16$ cm and the area of triangle $PSQ$ is 40 cm²,

1. **State the problem:** We need to find the furthest distance from the front of the stage (point D) where the lighting crew should place a mark so that any actor under 1.9 m tall

1. **State the problem:** We need to find the area of a right triangle with base $\sqrt{108}$ cm and height $4.8$ cm. 2. **Formula for the area of a triangle:**

1. **State the problem:** Find the area of a right triangle with height $48$ cm and base $\sqrt{108}$ cm. 2. **Formula for the area of a triangle:**

1. **State the problem:** We have a parallelogram with sides $a=6$ and $b=8$, and a diagonal of length $12$. We need to find the area $S$ and the height $H$ corresponding to side $

1. **Énoncé du problème :** Déterminer une équation cartésienne de la droite médiatrice du segment [AB] avec A(5,4) et B(3,6).

1. The problem asks: The smallest angle of a triangle is always opposite the ___________ side. 2. In any triangle, the size of an angle is directly related to the length of the sid

1. **State the problem:** Determine which sets of side lengths can form a triangle. 2. **Triangle inequality rule:** For any three sides $a$, $b$, and $c$ to form a triangle, the s

1. **State the problem:** Find the distance between the points $(-6, -3)$ and $(4, -7)$ using Pythagoras' theorem. 2. **Formula:** The distance $d$ between two points $(x_1, y_1)$

1. **State the problem:** We have a solid triangular prism with right-angled triangular bases. The base and height of the triangle are $20x$ cm and $15x$ cm respectively, and the h

1. **State the problem:** We have two right-angled triangles sharing a common hypotenuse $z$. The larger triangle has legs 12 cm and 14 cm, and the smaller triangle inside it has o

1. **Problem:** Find the area of a triangular plot of land with sides 240 ft, 300 ft, and 360 ft. 2. **Formula:** Use Heron's formula for the area of a triangle when all sides are

1. The problem is to find the area of a circle using a method suitable for primary six students. 2. The formula for the area of a circle is given by $$\text{Area} = \pi r^2$$ where

1. **Stating the problem:** We have two circles with radii 5 m and 4 m, and the distance between their centers is 6 m. We want to find the length of the line segment where the two

1. **Problem statement:** Given triangle ABC with sides AB = 10 m, BC = 12 m, AC = 29 m, and angles \(\angle A = 49^\circ\), \(\angle C = 35^\circ\), find \(\angle B\), perimeter \

1. **Problem Statement:** Find the area of the shaded part of the door, which is a circular area with diameter 2 ft inside a door of width 4 ft and height 10 ft. 2. **Formula Used:

1. **Problem Statement:** Determine if the two metro tracks (Line A and Line B) are parallel.

1. **State the problem:** We need to prove that triangle $\triangle EFX$ is congruent to triangle $\triangle GHX$ based on the given markings. 2. **Identify given information:**