Geometry
Problems related to shapes, spaces, measurements, etc.
Problems in this category
The problem is based on similar triangles $\triangle PXY$ and $\triangle PRQ$. We need to: a) Name a...
Similar TrianglesTriangle AreaRatiosGeometric Proofs
2025/3/31
The problem consists of three parts related to similar triangles $\triangle PXY$ and $\triangle PQR$...
Similar TrianglesTriangle AreaProportions
2025/3/31
In triangle $ABC$, $\angle B = 45^\circ$ and $\angle C = 75^\circ$. $D$ is the intersection of the a...
TrianglesLaw of SinesAngle BisectorCircumcenterTrigonometryGeometry Ratios
2025/3/31
The problem provides a diagram with $AEXD$ and $BFXC$ being straight lines. We are given the lengths...
Similar TrianglesParallel LinesTriangle CongruenceProportions
2025/3/31
We are given a diagram where $AEXD$ and $BFXC$ are straight lines. We are also given $AE = 2$ cm, $...
Similar TrianglesParallel LinesTriangle CongruenceTriangle SimilarityRatios and Proportions
2025/3/31
We are given a triangle $ABC$ with $AC = 3.5$ cm and $BE = 4.2$ cm. Also, $DE = 2.1$ cm and $\angle ...
Triangle SimilarityArea of TriangleProportionsAA Similarity
2025/3/31
We are given triangle $ABC$ with $AC = 3.5$ cm, $BE = 4.2$ cm, $DE = 2.1$ cm, and $\angle BAC = \ang...
Similar TrianglesTriangle AreaGeometric RatiosAA Similarity
2025/3/31
The problem states that in an isosceles triangle, the angle bisector of a base angle intersects the ...
TrianglesAngle BisectorsIsosceles TrianglesAngle Calculation
2025/3/31
The problem requires us to describe how a student would create a program to calculate the perimeter ...
PerimeterRectangleFormulaInput/OutputSolution Space
2025/3/31
Given a regular hexagon $ABCDEF$, and the vectors $\vec{AB} = \vec{m}$ and $\vec{BC} = \vec{n}$, exp...
VectorsHexagonGeometric VectorsVector AdditionRegular Polygons
2025/3/31