Which test can be used to prove that the given pair of triangles are similar?

Which test can be used to prove that the given pair of triangles are similar?

For the given pair of triangles

a) Complete Δ XYZ lll Δ ?
b) What is the name of similarity test

Which test can be used to prove that the given pair of triangles are similar?

In rectangle \(ABCD\), is \(\bigtriangleup BAD\, ||| \bigtriangleup DEC\)

Lucas wants to reduce a triangular pattern with sides 9 cm, 9 cm and 15 cm. If the longest side of the new pattern is to be 10 cm, how long should the other two sides be?

In the following diagram, \(PQ=7~\text{cm}\), \(ST=6~\text{cm}\) and \(PR=14~\text{cm}\)

a) Is \(\bigtriangleup PQR\,\,|||\bigtriangleup TSR\)?

b) What is the length of \(TR\)?

For the given pair of triangles

a. Complete \(Δ PQR \,|||\, Δ ?\)
b. What is the name of similarity test

Which test can be used to prove that the given pair of triangles are similar?

Which test can be used to prove that each pair of triangles are similar?

Which test can be used to prove that each pair of triangles are similar?

Bob's shadow is \(2.7 \text{ m}\) long while a \(1 \text{ m}\) shadow stick as a shadow of \(1.5 \text{ m}\).

Find Bob's height. 

Two similar triangles are created by cables supporting a yacht's mast. 

Find the height of the mast. 

A surveyor sights a tree on the opposite side of a river bank. He marks out \(4\) points as shown. 

Find the width of the river. 

Two cables support a pole at the same angle. 

Find the height of the pole. 

A \(3.7 \text{ m}\) ramp leans on a \(0.9 \text{ m}\) post. One end is on the ground and the other touches a vertical wall \(1.2 \text{ m}\) from the ground. 

i) Find the distance from the bottom of the ramp to the wall.

ii) Find how far the bottom of the ramp is from the post. (3 decimal places). 

A building that is \(32 \text{ m}\) high casts a shadow \(18 \text{ m}\) long. At the same time the shadow of a tree is \(4.5 \text{ m}\).

What is the height of the tree?

For \(\bigtriangleup PQR\)

a) Is \(\bigtriangleup PSQ\,\,|||\bigtriangleup RSP\)?

b) What is the length of \(SP\)?

In the following figure, \(PQ||RU\) and \(PT/PR=4/7\)

a) Are \(\bigtriangleup PST\) and \(\bigtriangleup RUT\) similar?

b) If \(UR=6~\text{cm}\) find \(SP\).

In \(\bigtriangleup ABC\)

a) What is the similarity proof for \(\bigtriangleup ADE\,\,|||\bigtriangleup ACB\)?

b)  If \(DE=5\), find \(BC\)?