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NYS Geometry Regents Exam Practice: Questions 28 & 29

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NYS Geometry Regents Exam Practice: Questions 28 & 29

Welcome back to our series on NYS Geometry Regents Exam practice! In this video, we’ll tackle questions 28 and 29 from a past exam. These questions are a great way to test your understanding of key geometry concepts, so let’s dive in.

Question 28: Proving Triangle Similarity

**The Problem:**

In the diagram below, △ABC is similar to △DEF. Find the length of side DF.

Diagram of similar triangles ABC and DEF

**Solution:**

Since the triangles are similar, their corresponding sides are proportional. This means:

AB/DE = BC/EF = AC/DF

We are given the lengths of AB, DE, BC, and EF. We need to find DF. Let’s plug in the values:

6/9 = 8/12 = AC/DF

Simplifying the first two ratios, we get:

2/3 = 2/3 = AC/DF

Therefore, AC/DF = 2/3. To solve for DF, we can cross-multiply:

2DF = 3AC

We are given that AC = 10, so:

2DF = 3(10)

2DF = 30

DF = 30/2

DF = 15

**Answer:** The length of side DF is 15.

Question 29: Finding the Area of a Triangle

**The Problem:**

The vertices of triangle ABC are A(2,1), B(8,1), and C(5,7). Find the area of triangle ABC.

**Solution:**

We can find the area of a triangle using the formula:

Area = (1/2) * base * height

Let’s consider side AB as the base of the triangle. The length of AB is 8 – 2 = 6 units. The height of the triangle is the perpendicular distance from point C to line AB.

Since AB is horizontal, the height is simply the difference in y-coordinates between C and any point on AB. We can use point A:

Height = 7 – 1 = 6 units

Now, we can plug in the values into the area formula:

Area = (1/2) * 6 * 6

Area = 18 square units

**Answer:** The area of triangle ABC is 18 square units.

Key Takeaways

These two questions demonstrate important concepts in geometry: similarity and area calculation. Remember to:

  • Understand the properties of similar triangles, including proportional sides.
  • Know how to calculate the area of a triangle using the base and height.
  • Practice applying these concepts to different types of problems.

Keep practicing with past Regents exams and other geometry resources. Good luck with your studies!

Regents Exam Prep