Bedrock Pro

Eric, creator of Bedrock and LearnSATMath

The complete SAT Math curriculum180+ videos and concept guides by Eric1010+ problems with written explanations

Angles & Trianglesmedium

77m

Similarity

In the figure shown, $\overline{JM}$ and $\overline{KL}$ intersect at point $P$ , $JP = 45$ , $LP = 18$ , $JK = 40$ , and $KP = 60$ . What is the length of $\overline{LM}$ ?

Note: Figure not drawn to scale.

Solution

Step 1. The figure marks angle $J$ and angle $L$ with the same $a^\circ$ . $\spotgreen{\angle JPK}$ and $\spotgreen{\angle LPM}$ are vertical angles, so they're equal too. Two matching angles are enough for similarity, so triangle $JKP$ is similar to triangle $LMP$ , with $J$ corresponding to $L$ , $K$ to $M$ , and $P$ to $P$ .

Segments JM and KL crossing at P, with the a-degree marks at J and L and the vertical angles at P arced in green

Step 2. Similar triangles are scaled copies, so every side is multiplied by the same number. Pair the sides by their endpoints. $J$ and $P$ match $L$ and $P$ , so $\spotred{\overline{JP}}$ corresponds to $\spotred{\overline{LP}}$ . $J$ and $K$ match $L$ and $M$ , so $\spotblue{\overline{JK}}$ corresponds to $\spotblue{\overline{LM}}$ .

The same figure with JP and LP in red labeled 45 and 18, and JK and LM in blue labeled 40 and a question mark

Step 3. The problem gives us $\spotred{JP} = 45$ and $\spotred{LP} = 18$ , so triangle $LMP$ is triangle $JKP$ scaled by $\dfrac{18}{45}$ . Call that number $k$ .

Step 4. Every side scales by that same $k$ , and the problem gives us $\spotblue{JK} = 40$ :

\spotblue{LM} = 40k

\displaystyle k = \frac{18}{45}

\displaystyle 40k

$\overline{LM}$ has a length of $16$ . Choice B.

Practice tests with detailed analyticsAll in an adaptive curriculum built around your weaknesses.

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Problem 125d: Margin of Error, medium, requires Bedrock Pro

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Ashley
610to760
“It’s genuinely the only website that teaches you how to crack Desmos perfectly. I raised my SAT math score by 150 points in just 2 weeks of using it. I CANNOT recommend it enough!”
Donatella
690to770
“Bedrock is an absolute game changer. Learning how to master Desmos and breaking down core problem types made everything click. Truly the only math prep platform you need!”
Aarian
690to780
“Bedrock increased my SAT math score over 100 points in a week! The site is so easy to use and the explanations all help so much. The pro version is definitely worth it if you want to go all in.”
Nikhila
650to790
“For some problems Desmos is the way to go, and for some you really shouldn’t use it. Bedrock makes that super clear. A lot of the questions I practiced were basically the same on the actual SAT. It’s one of the best things I ever did for my SAT.”
Myles
730to790
“The best thing about Bedrock are the expert level practice problems. My girlfriend studied with me and her math score jumped from a 580 to a 760 after a month with Bedrock.”
Parnav
650to800
“Bedrock is one of the best SAT prep tools out there. I started at a 650 on my first practice test and got my score all the way up to an 800 through doing the problems there!”
Omar
700to800
“Bedrock has literally all the types of questions you’ll probably encounter on the SAT math sections with Desmos solutions where possible. I really recommend it to anyone wanting to get a 780+ in maths.”
Hansel
690to750
“Bedrock helped SO much. I personally struggle with a very low attention span (thanks insta reels), and the way Bedrock made the questions seem gamified helped me literally pick up SAT math questions when I was bored.”
Eslam
630to710
“Bedrock helped me improve my SAT Math score from 630 in August to 710 in September in just about a week of studying. I really liked how it focuses on the harder questions, explains them clearly, and puts a lot of emphasis on using Desmos effectively.”
Katelyn
630to730
“I didn’t realize how useful Desmos could be on the math SAT problems, but these practice problems with the video explanations in the Bedrock 125 were very clear and understandable. My math score went up by 100 on the practice SAT.”
Alyazyah
360to410
“The way the app is designed makes it easy for me to know what topic to move onto next. I did a practice test and got 360, and using Bedrock for one day has allowed me to get 410 in a math practice test!”
Dash
790
“Bedrock truly is a gem and I would recommend it to anyone who needs SAT math help. With this tool, I was able to increase my math score to 790, something I didn’t think was possible after the June SAT.”
Ana
630to760
“As someone who doesn’t typically find math easy, I was amazed at how Bedrock 125 made even the hardest SAT problems seem simple. In just nine weeks, I improved my math score by 130 points.”
Ahmad
630to700
“Hands down the best SAT Math curriculum available. Big-box prep might get you across the baseline, but if you want to jump into the 1400–1500+ tier, this is it. I went from a shaky, lucky 630 diagnostic to a legitimate 700 on the official SAT.”
Naomi
680to780
“Bedrock was genuinely a LIFESAVER. I tried so many other resources, but there was nothing as effective as Bedrock. It helped me target my weaknesses and exposed me to problems I had genuinely never seen before.”
Andrea
610to740
“I improved 130 math points in TWO WEEKS, giving me an amazing score, because Eric remembers that math is improved by being understood and not memorized. That is Bedrock 125.”
Chance
600to730
“I went from scoring 1200 to scoring 1440 on the official SAT just by using Desmos tricks learned from this site!”
Kunal
640to750
“In two weeks of practice, I managed to get a 110 point increase on the SAT, getting a 750, and I can confidently attribute that to Bedrock. Trust me when I say, Bedrock really does have it all.”
Bryce
510to670
“The solution steps for each problem type I got wrong really helped me to point out my errors and make way fewer mistakes. It got me from a 1050 to a 1310, so I definitely recommend using this program to study for the SAT.”
Carter
540to670
“Bedrock helped me review and further understand how to quickly and properly solve math problems I hadn’t looked at in years. It also helped me understand how to properly use the Desmos calculator to my advantage, and ultimately made me a lot more comfortable with the math section of the SAT.”
Adrian
640to730
“The explanations and videos helped me fill in the gaps for problems I was struggling on, and the practice tests were quite realistic of a real SAT.”
Tim
750to790
“Bedrock Pro is a one-of-a-kind tool for studying. There are dozens of questions per math subsection, of varying difficulty, allowing students to target their weak points with questions that get progressively more difficult.”
Tom
680to780
“Pretty darn awesome site. Really struggled with math at first, but I was able to isolate the exact topics I needed to work on.”
Patrick
590to750
“It works so well I can’t lie.”
John
680
“I was enrolled in a thousand dollar SAT course before Bedrock, but it wasn’t able to help in the math section close to how Bedrock does.”
Niguilo
730to800
“Hands down best SAT Math resource out there.”
Aayrah
650to740
“I absolutely LOVE Bedrock. It’s easy to use, worth the price, and completely transformed my confidence!”
Emily
600to740
“I really enjoyed using Bedrock for math. The program helped improve my score by 100+ points!”
Ignacio
710to780
“Offers all of the questions that can come up in the SAT. Really helped me improve with the additional questions!”
Kaitlyn
670to770
“It helped me learn new tricks which saved me so much time.”
Timothy
“I have been hunting SAT prep courses for many months and this one has hit the mark! The course schedule plus practice problems and tests are all great in themselves, but what makes Bedrock stand out is that the problem explanations are very thorough and many times in a video format.”
Asmi
690to760
“Bedrock really had a wide variety of problems and solutions that helped me improve.”

Ashley
610to760
“It’s genuinely the only website that teaches you how to crack Desmos perfectly. I raised my SAT math score by 150 points in just 2 weeks of using it. I CANNOT recommend it enough!”
Donatella
690to770
“Bedrock is an absolute game changer. Learning how to master Desmos and breaking down core problem types made everything click. Truly the only math prep platform you need!”
Aarian
690to780
“Bedrock increased my SAT math score over 100 points in a week! The site is so easy to use and the explanations all help so much. The pro version is definitely worth it if you want to go all in.”
Nikhila
650to790
“For some problems Desmos is the way to go, and for some you really shouldn’t use it. Bedrock makes that super clear. A lot of the questions I practiced were basically the same on the actual SAT. It’s one of the best things I ever did for my SAT.”
Myles
730to790
“The best thing about Bedrock are the expert level practice problems. My girlfriend studied with me and her math score jumped from a 580 to a 760 after a month with Bedrock.”
Parnav
650to800
“Bedrock is one of the best SAT prep tools out there. I started at a 650 on my first practice test and got my score all the way up to an 800 through doing the problems there!”
Omar
700to800
“Bedrock has literally all the types of questions you’ll probably encounter on the SAT math sections with Desmos solutions where possible. I really recommend it to anyone wanting to get a 780+ in maths.”
Hansel
690to750
“Bedrock helped SO much. I personally struggle with a very low attention span (thanks insta reels), and the way Bedrock made the questions seem gamified helped me literally pick up SAT math questions when I was bored.”
Eslam
630to710
“Bedrock helped me improve my SAT Math score from 630 in August to 710 in September in just about a week of studying. I really liked how it focuses on the harder questions, explains them clearly, and puts a lot of emphasis on using Desmos effectively.”
Katelyn
630to730
“I didn’t realize how useful Desmos could be on the math SAT problems, but these practice problems with the video explanations in the Bedrock 125 were very clear and understandable. My math score went up by 100 on the practice SAT.”
Alyazyah
360to410
“The way the app is designed makes it easy for me to know what topic to move onto next. I did a practice test and got 360, and using Bedrock for one day has allowed me to get 410 in a math practice test!”
Dash
790
“Bedrock truly is a gem and I would recommend it to anyone who needs SAT math help. With this tool, I was able to increase my math score to 790, something I didn’t think was possible after the June SAT.”
Ana
630to760
“As someone who doesn’t typically find math easy, I was amazed at how Bedrock 125 made even the hardest SAT problems seem simple. In just nine weeks, I improved my math score by 130 points.”
Ahmad
630to700
“Hands down the best SAT Math curriculum available. Big-box prep might get you across the baseline, but if you want to jump into the 1400–1500+ tier, this is it. I went from a shaky, lucky 630 diagnostic to a legitimate 700 on the official SAT.”
Naomi
680to780
“Bedrock was genuinely a LIFESAVER. I tried so many other resources, but there was nothing as effective as Bedrock. It helped me target my weaknesses and exposed me to problems I had genuinely never seen before.”
Andrea
610to740
“I improved 130 math points in TWO WEEKS, giving me an amazing score, because Eric remembers that math is improved by being understood and not memorized. That is Bedrock 125.”
Chance
600to730
“I went from scoring 1200 to scoring 1440 on the official SAT just by using Desmos tricks learned from this site!”
Kunal
640to750
“In two weeks of practice, I managed to get a 110 point increase on the SAT, getting a 750, and I can confidently attribute that to Bedrock. Trust me when I say, Bedrock really does have it all.”
Bryce
510to670
“The solution steps for each problem type I got wrong really helped me to point out my errors and make way fewer mistakes. It got me from a 1050 to a 1310, so I definitely recommend using this program to study for the SAT.”
Carter
540to670
“Bedrock helped me review and further understand how to quickly and properly solve math problems I hadn’t looked at in years. It also helped me understand how to properly use the Desmos calculator to my advantage, and ultimately made me a lot more comfortable with the math section of the SAT.”
Adrian
640to730
“The explanations and videos helped me fill in the gaps for problems I was struggling on, and the practice tests were quite realistic of a real SAT.”
Tim
750to790
“Bedrock Pro is a one-of-a-kind tool for studying. There are dozens of questions per math subsection, of varying difficulty, allowing students to target their weak points with questions that get progressively more difficult.”
Tom
680to780
“Pretty darn awesome site. Really struggled with math at first, but I was able to isolate the exact topics I needed to work on.”
Patrick
590to750
“It works so well I can’t lie.”
John
680
“I was enrolled in a thousand dollar SAT course before Bedrock, but it wasn’t able to help in the math section close to how Bedrock does.”
Niguilo
730to800
“Hands down best SAT Math resource out there.”
Aayrah
650to740
“I absolutely LOVE Bedrock. It’s easy to use, worth the price, and completely transformed my confidence!”
Emily
600to740
“I really enjoyed using Bedrock for math. The program helped improve my score by 100+ points!”
Ignacio
710to780
“Offers all of the questions that can come up in the SAT. Really helped me improve with the additional questions!”
Kaitlyn
670to770
“It helped me learn new tricks which saved me so much time.”
Timothy
“I have been hunting SAT prep courses for many months and this one has hit the mark! The course schedule plus practice problems and tests are all great in themselves, but what makes Bedrock stand out is that the problem explanations are very thorough and many times in a video format.”
Asmi
690to760
“Bedrock really had a wide variety of problems and solutions that helped me improve.”

8 levels, 106 topics

Every student falls into one of 8 levels. Each level walks you through the lessons, drills, and problems built around your weaknesses, taking you up to the next level.

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Explanations for all 1010 problems

Every Pro problem comes with a full written solution, showing the optimal approach(es) for each problem. Unlike most platforms, Bedrock solutions always include Desmos when applicable.

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