Question

1. \\(\delta abc \sim \delta dec\\)

find the length of \\(\overline{bc}\\).

\\(\overline{bc} = \underline{\quad\quad\quad}\\)

1. find the measures of \\(\angle a\\) and \\(\angle e\\).

then, name the pairs of similar triangles and write the scale factor of the larger triangle to the smaller for each triangle pair.

\\(\angle a = \underline{\quad\quad\quad}\\)
\\(\angle e = \underline{\quad\quad\quad}\\)

similar \\(\delta\\)s and scale factor:
\\(\underline{\quad\quad\quad}\\)
\\(\underline{\quad\quad\quad}\\)
\\(\underline{\quad\quad\quad}\\)

Explanation:

Find the length of BC in Question 9

Using the Geometric Similarity and Scale Factor knowledge points

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Find the measure of angle A in Question 10

Using the Triangle Angle Sum Theorem and Vertical Angles Theorem knowledge points

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Find the measure of angle E in Question 10

Using the Triangle Angle Sum Theorem and Vertical Angles Theorem knowledge points

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Identify similar triangles in Question 10

We compare the angles of the triangles in the figure:

• For \(\Delta ABC\): the angles are \(24^\circ\), \(92^\circ\), and \(64^\circ\).
• For \(\Delta FCD\): \(\angle FCD = 64^\circ\), \(\angle D = 24^\circ\), so \(\angle CFD = 180^\circ - 64^\circ - 24^\circ = 92^\circ\).
• Since \(\Delta ABC\) and \(\Delta FCD\) have corresponding angles of \(24^\circ\), \(92^\circ\), and \(64^\circ\), they are similar by AA Similarity.
• The correct vertex correspondence is \(\Delta ABC \sim \Delta DFC\).

Calculate the scale factor for the similar pair

Using the Scale Factor knowledge point

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Answer:

Question 9

\(\overline{BC} = 0.95\)

Question 10

\(\angle A = 24^\circ\)

\(\angle E = 75^\circ\)

Similar \(\Delta\)s and Scale factor:
\(\Delta ABC \sim \Delta DFC\) with a scale factor of \(3\) (or \(3:1\))