# Solving Problems with Similar and Congruent Triangles

When navigating geometric problem-solving, understanding the principles of similar and congruent triangles is pivotal. These fundamental concepts provide a framework for analyzing and resolving various mathematical challenges efficiently. Similar triangles possess corresponding angles of equal measure and proportional side lengths, while congruent triangles exhibit identical angles and side lengths. Mastery of these properties empowers problem solvers to apply geometric principles accurately, whether in determining unknown dimensions, proving theorems, or constructing geometric figures. By leveraging the properties of similar and congruent triangles, individuals can adeptly navigate a myriad of geometric problem-solving scenarios with precision and efficacy.

- Are two isosceles triangles always similar? Are two equilateral triangles always similar? Give reasons for your answers to both questions.
- In the figure given identify the congruent and/or similar triangles and find the value of x and y?
- Can the sides of a triangle have lengths 17, 7, and 18?
- Given the figure determine the value of the unknown segment, #x#?
- If two triangles are congruent, are they similar? Please explain why or why not.
- In the diagram, BC¯¯¯∥DE¯¯¯ What is CE ?
- Can the sides of a triangle have lengths 1, 2, and 8?
- You have two similar triangles. The first triangle has a height of 10 and an area of 40. If the second triangle is twice as tall, how much area does it cover?
- How many congruent sides does a regular hexagon have?
- For which segment lengths is ¯¯¯AC¯ parallel to ¯¯DE¯ ?
- Find the value of x for each of the given figures?
- How Can Ken use Similar Triangles to find the height of a Building?
- Comparing the two parallelograms, which of the following is not necessarily true?
- Why can't there be an axiom of congruency of triangles as A.S.S. similar to R.H.S.?
- Find the value of x in the figure?
- How do you approximate the height of the screen to the nearest tenth?
- Given the similar right triangles in the figure. Find the exact values of x and y?
- What are the differences between similar triangles and congruent triangles?
- (a) Can Kayla conclude that and are similar? Why or why not? (b) Suppose DE = 32 ft. What can Kayla conclude about the width of the river? Explain.
- Nathan cut an isosceles triangle from felt to make a spirit banner. Two sides of his banner had the following measures : 15 inches and 7 inches. Which could be the measure of the third side of Nathan’s banner ? A. 20 b. 15 c. 10 d. 7