Similarity & Congruence

Two triangles are said to be congruent if ...

Two plane figures are called similar when ...

Triangle $ABC$ is similar to triangle $PQR$, with $AB$ corresponding to $PQ$ and $BC$ to $QR$. If $AB=3\text{cm}$, $BC=4\text{cm}$, and $PQ=6\text{cm}$, the length of $QR$ is ...

If $△ABC\cong △PQR$, the angle equal to $\angle A$ is ...

Which pair of figures is always similar?

Two similar triangles have a side ratio of $1:2$. If the shortest side of the smaller triangle is $5\text{cm}$, the shortest side of the larger triangle is ...

Triangle $ABC$ is right-angled at $B$ and triangle $PQR$ is right-angled at $Q$. If $\angle A=\angle P$, then ...

In $△ABC$, point $D$ lies on $AB$ and point $E$ on $AC$ with $DE\parallel BC$. Given $AD=4\text{cm}$, $DB=6\text{cm}$, and $DE=8\text{cm}$, the length of $BC$ is ...

Given $△ABC$ and $△DEF$ with $AB=DE$, $BC=EF$, and $\angle B=\angle E$. The two triangles are congruent by the ... condition.

Two similar triangles have a side ratio of $2:3$. The ratio of their areas is ...

A $2\text{m}$ pole casts a $3\text{m}$ shadow. At the same time, a tree casts a $12\text{m}$ shadow. The height of the tree is ...

On a map with a scale of $1:500,000$, the distance between two cities is $4\text{cm}$. The actual distance between them is ...

A triangle with sides $5\text{cm}$, $6\text{cm}$, and $7\text{cm}$ is congruent to a triangle whose sides are ...

Two similar figures have an area ratio of $25:36$. The ratio of their corresponding side lengths is ...

In $△ABC$, $D$ lies on $AB$ and $E$ on $AC$ with $DE\parallel BC$. If $AD=x\text{cm}$, $DB=(x+2)\text{cm}$, $AE=3\text{cm}$, and $EC=5\text{cm}$, the value of $x$ is ...

Two similar triangles have areas $16{\text{cm}}^2$ and $36{\text{cm}}^2$. If the perimeter of the smaller triangle is $24\text{cm}$, the perimeter of the larger triangle is ...

Two similar triangles have a side ratio of $3:5$. If the sum of their areas is $136{\text{cm}}^2$, the area of the larger triangle is ...

The height of a tower in a model is $24\text{cm}$ with a scale of $1:150$. The actual height of the tower is ...

A photo measuring $3\text{cm}\times 4\text{cm}$ is enlarged proportionally so that its width becomes $15\text{cm}$. The area of the enlarged photo is ...

Triangle $ABC$ is similar to $△PQR$, with $AB$ corresponding to $PQ$ and $BC$ to $QR$. Given $AB=8\text{cm}$, $BC=10\text{cm}$, $PQ=12\text{cm}$, and $QR=(2x-1)\text{cm}$, the value of $x$ is ...