Geometry
Problems related to shapes, spaces, measurements, etc.
Problems in this category
We are given a triangle with a line segment inside that is parallel to one of the sides. We are give...
TrianglesParallel LinesAngle PropertiesAlgebra
2025/4/1
The problem asks to find the values of $x$ and $y$ in the given figure, where three parallel lines a...
Parallel LinesAnglesTransversalCorresponding AnglesAlgebraic Equations
2025/4/1
We are given a figure with two parallel lines $p$ and $q$, intersected by transversals $j, k, m, n$....
Parallel LinesAnglesTransversalsCorresponding AnglesSupplementary Angles
2025/4/1
We are given a diagram with lines $j$, $k$, $m$, $n$, $p$, and $q$. We know that $m\angle 1 = 50^\ci...
AnglesParallel LinesTransversalsSupplementary AnglesVertical AnglesCorresponding Angles
2025/4/1
Given that $m\angle 9 = 75^{\circ}$, find the measure of the following angles: $\angle 3$, $\angle 5...
AnglesParallel LinesTransversalsCorresponding AnglesVertical AnglesSupplementary Angles
2025/4/1
The image shows a right triangle $\triangle LMN$ with a right angle at $L$. Point $P$ is on $NM$ suc...
Similar TrianglesRight TrianglesGeometric MeanProportions
2025/4/1
We are given a triangle $PQR$ with a line segment $YX$ parallel to $QR$. The length of $PY$ is 2, th...
Similar TrianglesProportionsParallel LinesTriangle Properties
2025/4/1
We are given a right triangle FGH, where angle G is a right angle. The length of the side FH is 98, ...
TrigonometryRight TrianglesSineAnglesArctangent
2025/4/1
We are given a right triangle $KLM$ with a right angle at $L$. We are given that side $LM$ has lengt...
TrigonometryRight TrianglesCosineTriangle GeometryAngle Measurement
2025/4/1
We are given a triangle $LMN$ with a right angle at $L$. $LP$ is perpendicular to $NM$. We are given...
Similar TrianglesRight TrianglesProportionsPythagorean Theorem (implicitly used)
2025/4/1