Suggested languages for you:

Americas

Europe

Problem 246

The lengths of the sides of a triangle are 6,8, and 12 . The lengths of the sides of a second triangle are \(1(1 / 2), 2\), and 3 . Are the two triangles similar?

Expert verified

The two triangles are similar because the ratios of their corresponding sides are equal: \(\frac{6}{1\frac{1}{2}} = \frac{8}{2} = \frac{12}{3} = 4\).

What do you think about this solution?

We value your feedback to improve our textbook solutions.

- Access over 3 million high quality textbook solutions
- Access our popular flashcard, quiz, mock-exam and notes features
- Access our smart AI features to upgrade your learning

Chapter 13

In the accompanying figure, points \(D, E\), and \(F\) are points on the triangle \(\triangle \mathrm{ABC}\) such that $\underline{\mathrm{AD}}, \underline{\mathrm{BE}}\(, and \)\underline{\mathrm{CF}}$ are concurrent at point P. Show that $$ (\mathrm{BD} / \mathrm{DC})(\mathrm{CE} / \mathrm{EA})(\mathrm{AF} / \mathrm{FB})=1 $$

Chapter 13

Show that a regular pentagon and the pentagon determined by joining all the vertices of the regular pentagon are similar.

Chapter 13

(a) In \(\triangle \mathrm{ABC}\), if \(\mathrm{D}\) is the midpoint of \(\underline{\mathrm{AB}}, \mathrm{E}\) is the midpoint of \(\underline{\mathrm{AC}}\), and \(\mathrm{F}\) is the midpoint of \(\underline{\mathrm{BC}}\), then prove that $\underline{\mathrm{DE}} \| \mathrm{BC}$, \(\underline{E P} \| \underline{A B}\), and \(D P \| A C\). (b) Prove that \(\triangle \mathrm{DEF} \sim \Delta \mathrm{CBA}\).

Chapter 13

Given; \(\underline{A D}\) is an angle bisector of \(\triangle \mathrm{ABC} ;\) point \(\mathrm{E}\) is on \(\underline{\mathrm{AD}}\) such that $\mathrm{AB} \cdot \mathrm{AC}=\mathrm{AD} \cdot \mathrm{AE}\(. Proves \)\phi \mathrm{B} \cong<\mathrm{AEC}$.

Chapter 13

Given the A.A.A. (Angle, Angle, Angle) Similarity Theorem, prove the A.A. (Angle, Angle) Similarity Theorem.

The first learning app that truly has everything you need to ace your exams in one place.

- Flashcards & Quizzes
- AI Study Assistant
- Smart Note-Taking
- Mock-Exams
- Study Planner